The Kitzur Shulchan Aruch (128:2, end) brings down this minhag as follows:
מִשֶנִּכְנַס אֱלוּל עַד יוֹם הַכִּפּוּרִים, כְּשֶׁכּוֹתֵב אָדָם אִגֶּרֶת לַחֲבֵרוֹ, צָרִיךְ לִרְמֹז בָּהּ בִּתְחִלָּתָהּ אוֹ בְסוֹפָהּ שֶׁהוּא מְבַקֵּשׁ עָלָיו וּמְבָרְכוֹ, שֶׁיִּזְכֶּה בִּימֵי הַדִּין, הַבָּאִים לְטוֹבָה, לְהִכָּתֵב וּלְהֵחָתֵם בְּסֵפֶר חַיִּים טוֹבִים
From the beginning of Elul until Yom Kippur, when a man writes a letter to his friend, he must hint in it either at its beginning or at its end that he is asking for him and blesses him, that he should succeed in the days of judgement, which are coming for good, that he should be written and sealed in the book of good life. (translation and emphasis mine, Hebrew text copied from Sefaria)
It sounds to me that it doesn’t really matter the wording that one uses, as long as the general idea gets across.
Contrast this to the greeting we use on Rosh Hashanah night, which the Kitzur discusses in 129:8:
לְאַחַר גְּמָר תְּפִלַּת מַעֲרִיב בְּלֵיל רִאשׁוֹן, נוֹהֲגִין לוֹמַר כָּל אֶחָד לַחֲבֵרוֹ, לְשָׁנָה טוֹבָה תִּכָּתֵב וְתֵחָתֵם. וְלִנְקֵבָה אוֹמְרִים, תִּכָּתֵבִי וְתֵחָתֵמִי.
After Maariv is finished on the first night [of RH], it is customary for everyone to say to his friend, “For a good year may you be written and sealed [תכתב ותחתם],” and to a woman we say, “may you be written and sealed [תכתבי ותחתמי].” (translation still mine, Hebrew still Sefaria’s)
Unlike the greeting during Elul, in this greeting he is very particular about the wording being used, that it reflect the gender of the person being addressed. (The Artscroll Machzor adds two other greetings, for a group of men - תכתבו ותחתמו - and for a group of women - תכתבנה ותחתמנה - though I don’t have an earlier source that expands this idea to number in addition to gender. I think the logic holds anyway.)
So it would seem to me that regarding כתיבה וחתימה טובה, it would be fine to use whatever wording you want, regardless of how many people or of what gender they are to whom you’re extending the blessing, at least according to the Kitzur.
That said, if you want to be grammatically correct anyway, even if it doesn’t matter...
The reason the Rosh Hashanah night greetings are conjugated the way they are - by changing the gender and number of the verb to reflect the audience - is because you’re using verbs (תכתב ותחתם). In the common Elul greeting, the formulation uses nouns instead (כתיבה וחתימה), and nouns almost never switch between gender depending on the audience (there are exceptions, but those are few and far between, and I believe they only exist in Biblical Hebrew, not medieval and certainly not modern). While adjectives do change gender in addition to number, that’s to reflect the noun they’re modifying; they don’t change to reflect the audience directly. Therefore, you only have to worry about the number, and as such, you would change it the way you suggested in the question - כתיבות וחתימות טובות, regardless of the gender of the audience.