Kabbalistic literature in general, and chassidism in particular, contains teachings about tzaddikim that may be somewhat innovative from the perspective of traditional Judaism. However, the importance of the greatest rabbis of each generation is clear in Tanakh and Talmud, and there are some ancient sources supporting the exalted position of the tzaddik in chassidic philosophy.
For example, from the Jerusalem Talmud (Eruvin 5:1): "All the standing that the prophet Elijah did before his teacher Achiya Hashiloni, were as if standing before the Shekhinah."
In Pirkei Avos, we see this extraordinary statement, which could be interpreted to refer to the stature and power of a great tzaddik:
"Rabbi Meir would say: Whoever studies Torah for Torah's sake alone, merits many things; not only that, but [the creation of] the entire world is worthwhile for him alone. He is called friend, beloved, lover of G-d, lover of humanity, rejoicer of G-d, rejoicer of humanity. The Torah enclothes him with humility and awe; makes him fit to be righteous, pious, correct and faithful; distances him from sin and brings him close to merit. From him, people enjoy counsel and wisdom, understanding and power, as is stated (Proverbs 8:14): 'Mine are counsel and wisdom, I am understanding, mine is power.' The Torah grants him sovereignty, dominion, and jurisprudence. The Torah's secrets are revealed to him, and he becomes as an ever-increasing wellspring and as an unceasing river. He becomes modest, patient and forgiving of insults. The Torah uplifts him and makes him greater than all creations" (Pirkei Avos 6:1).
If a tzaddik can give people "power," can exercise "sovereignty" and "dominion," and is even "greater than all creation," it is conceivable that the spiritual attainments of ordinary people are dependent on connecting themselves to such tzaddikim. Thus, this may be one possible source of the elements of chassidic theology that you identify.
In addition, Mishlei 10:25 says וְצַדִּיק יְסוֹד עוֹלָם, which can be translated as the "Tzaddik is an everlasting foundation," or as the "Tzaddik is the foundation of the world."
For a Chabad perspective on the importance of tzaddikim in our avodas Hashem, see this essay: http://www.chabad.org/library/article_cdo/aid/137090/jewish/Tzaddik-The-Baal-Teshuvah.htm
The essay provides these two sources, in addition to others:
"The Rambam, based on the words of the Talmud, asks, 'How is it possible that one should cleave to G-d? G-d is fire and we are physical. One who touches fire will burn.' The Sages answer,'‘To cleave unto Him’ means that we should cleave to wise men and to their disciples,' i.e., tzaddikim. We cleave through connection with a tzaddik, who is one with G-d. Furthermore, believing in tzaddikim is based on a verse in Exodus said every day in our morning prayers:'[The Jews] believed in G-d and Moses His servant.' The Mechilta12 queries,'Why is it important to tell us that the Jewish people believed in Moses His servant? How can we equate our faith in Moses with our belief in G-d?' The answer is, without faith in Moses, or the Moses of every generation, there cannot be belief in G-d."
Non-chassidic sources also speak of the great importance of tzaddikim. R' Chaim of Volozhin, for example, writes that a tzaddik is "the beis hamikdah himself." (Nefesh haChaim 1:4).
In further researching this topic, keep in mind that in the Gemara, the term "chassid" is often used when we would use the term "tzaddik" today.
Finally, note that even if you find some aspects of chassidic thought (or Breslov chassidus) to be difficult to accept, you can still benefit from some of its teachings and practical advice, without adopting all the beliefs and practices it contains. A number of non-chassidic rabbis have learned chassidus and been influenced by it in some way or other, while continuing to adhere to the customs and hashkafic norms of non-chassidic Ashkenazim.
For example, see the quotes on this page, which show that several well-known non-chassidic rabbis, such as the Steipler Gaon, R' Eliyahu Dessler, R' Elya Lopian, praised and/or cited the teachings of Rebbe Nachman of Breslov: http://www.breslev-midot.com/eng/hillulat_moharahn_2005.asp.