Am I understanding this text properly, from the appropriate Jewish point of view [...] ?
Yes, the traditional Jewish understanding is indeed the one you (and the other contributors) presented; namely, that the various customs and rituals detailed in the Torah are to be observed unchanged and to the letter for all eternity; this has certainly been the consistent Pharisaic, Talmudic, and Rabbinic approach over the past two and a half millennia.
are my arguments against the Christian misinterpretation useful ?
Useful to whom ? To you (and other fellow Jews), or to the Christians mentioned above ? If the former, yes; if the latter, no, because their understanding of change would significantly differ from yours. This is ultimately due to historical considerations preceding Christianity by centuries, and utterly unrelated to its very existence (which they eventually helped shape anyway); specifically, it is because of the drastic difficulties faced by many ancient Diaspora Jews in efficiently implementing what one would call a kosher lifestyle whilst living in exile among the various Gentile nations.
This can be seen both in the Babylonian era book of Daniel, found among the canonical scriptures, as well as in the pious, though non-canonical, book of Tobit, penned in Hellenistic times. In both cases, their main protagonists are presented as pious Jews, steadfastly holding on to ancestral customs, despite harsh realities; needless to say, this is done for a reason; namely, the steady decline in observance among the Hebrews in general, whose piety these texts were meant to revive in the first place.
Granted, this can be (partially) explained by the general (leit)motif reverberating throughout scripture as a whole, namely Israel's general disinterest in the Torah; but, this time, it goes even deeper, inasmuch as there is only a (very) limited amount of control that one can exercise over external realities independent of oneself, such as the provenance of meats sold at a marketplace, for instance, or the uncertainty surrounding their possible previous involvement in certain pagan feasts or sacrifices.
These down to earth, day to day, practical and pragmatic issues marked the beginning of a major historical rift between Diaspora and Israeli Jews in terms of Torah observance, upon which, in Judaism, one's righteousness, and therefore one's share in the world to come, is ultimately predicated. Is it either just or right(eous) for two persons, equally strong in their desire to fulfill the commandments, to be either barred from or welcomed into eternal life because of ultimately geographic considerations, lying well beyond their power of control ?
Therefore, to gain some sort of semblance of self-respect, the Hebrew Diaspora logically sought spiritual solace, comfort, and refuge in a righteousness whose attainment is unencumbered by the above-listed hindrances; this happened under the influence of (mainly Greek) philosophy, which saw in the physical, material, transient, and impermanent world figures or symbols of eternal, unchanging realities; one of its most accomplished exponents being Philo of Alexandria, a contemporary of early Christianity. Speaking of which, let us now finally turn our attention to the aforementioned quote from Jeremiah (31:31-34):
Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah. [...] I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
In light of the preceding paragraphs, let us now parse this passage through the eyes of an ancient Diaspora Jew, echoing Philo's Greek philosophical ideas, rather than the ones espoused by homeland Israelis of the Second Temple period, which have already been presented in the other answers. For starters, let us note that a very similar message is being conveyed elsewhere in scripture; namely, in Ezekiel (36:26-27), which reads as follows:
A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh. And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them.
So, how would such a Jew, living under the above-described circumstances, be tempted to interpret these sacred Hebrew texts ? Would he feel in any way inclined to render them as referring to, or even favoring a literal fulfilling of the divine commandments ? As literal as the literal stones upon which they were literally carved, and which Moses literally broke in anger, when witnessing their wayward hearts worship the golden calf ? Given that both seem to employ a metaphorical, rather than literal language (write in their hearts, heart of stone, and other similar expressions), an initial attempt would be to render them as describing spiritual, rather than physical realities (I will give you a new spirit, I will put my spirit within you, etc.), in concordance and conformity with the all-pervading Greek philosophical thought of their time; such a predisposition would then only have been further strengthened, apart from the vicissitudes hurdled in their day to day struggle (and failure) to literally keep the Torah, by yet other verses in the same vein, whether within Jeremiah:
Jeremiah 4:4 Circumcise yourselves to the LORD, and take away the foreskins of your heart, ye men of Judah and inhabitants of Jerusalem.
or even within the Torah itself:
Deuteronomy 10:16 Circumcise therefore the foreskin of your heart, and be no more stiff-necked. 30:6 And the LORD thy God will circumcise thine heart, and the heart of thy seed, to love the LORD thy God with all thine heart, and with all thy soul, that thou may live.
Needless to say, similar echoes are found in early Christian literature; specifically, in Paul's letters (Romans 2:28-29), aimed particularly at captivating precisely such a Hellenized Jewish audience (following the persecutions against the then-new religious faith within the Hebrew homeland), and where the focus is, by the sheer virtue of necessity, shifted towards an inner, rather than an outer keeping of the commandments, since the same difficulties were faced by all Hebrews living in the Diaspora, regardless of their stance on Christianity.
But how can the heart be circumcised ? Certainly not literally, least one's desire to fulfill or obey such a divine decree would inadvertently lead one to breaking one of the ten commandments, namely the sixth; as such, let us appeal to philosophy: What eternal, spiritual reality does the physical act of circumcision stand for ? The cutting away of one's lust, for instance ? Yes, the above-mentioned Hellenist would say, and the entire Tanakh appears to echo this view:
Within Genesis itself, Lamech and Esau, unlike Abraham or Jacob, for instance, took two wives for themselves, from the very beginning, without any need or provocation; we all know how their two stories would eventually end.
Moses himself prohibits various types of sexual immorality in his other four books, threatening to punish such transgressions by stoning, no less.
In the books of Samuel and Kings, David looked upon Uriah's wife, Bathsheba, whilst she was having a bath, and Solomon married hundreds upon hundreds of wives and concubines; needless to say, their acts also had dire implications for everyone involved.
It is in this manner that Hellenized Judaism (and Christianity, afterwards), would (re)interpret the Laws of the Mosaic covenant; even their Pharisaic, Talmudic, and Rabbinic counterparts would be ultimately forced to make certain concessions; such as, for instance, the traditional Jewish (re)interpretation of fasting as a sacrifice of (one's own) flesh and blood, in the absence of a Temple, due to the practitioner's inherent self-emaciation. What initially began as an unfortunate accident of fate would eventually, over millennia, imbue the various branches of Judaism with a deeply internalized philosophical outlook and enriched spiritual perspective, rivaling even that of the ancient Greeks; Solomon and Socrates, hand in hand, at times both wrestling and cooperating with one another.
I sincerely hope that my humble effort, which can in no way substitute itself for a thorough incursion into the sinuous history of Jewish religious thought, nor meaningfully replace a serious reading of Philo, will help dispel at least some of your inner conflicts, mentioned in your question, over how Jews and Christians sometimes seem to approach the same biblical texts from widely different angles. When studying evolution, whether biological or ideological (and religious), the key lies in finding the missing (historical) link, tying together the wide diversity in variation exhibited by the various present-day species or specimens.