“It stands to reason that in order to be an ikar hadas that disbelieving it is tantamount to heresy, there must be an overwhelming significance to the principle.”
This seemingly obvious axiom is what brings about the confusion that follows.
” It stands to reason..” – I would like to humbly suggest that these discussions while being bound to reason, are not founded upon reason. It is only founded on what is known and demonstrated to be true. Since it is easily established that the full truth is both unknown to us and unknowable by it’s very existence, we then allow ourselves to expand it by other knowledgeable means. (Whether that is by tradition, logic, the senses, or even guesswork, is not consequential at this early point.)
(*The OP assumes that The Ikkarim are individual ikari hadas. But this seems to be debatable in the course of the thread. I’m not sure if it matters to the follow up points in the OP.)
“…disbelieving…” This needs a clear citation. We are not Jews because of any basic beliefs or founding statement. We are Jews because of our commitment to act our lives as commanded to us by The Torah. Having erroneous beliefs will cripple a basic understanding of Torah. It will not hinder a Jew from fulfilling our common duties.
I’m not advocating C”V for any negation, of what we know and believe as true. My only question is that are we correct to equate our Ikkarim with other systems (even reasonable ones) that demand an obedience to statute with no meaningful application. Just because one does not know/understand/internalize/concur to all The Ikkarim, Jews do not call that heresey. Or at least, it does not equate to one fully concurs with all the Ikkarim, yet serves idols or invents his own religious practices.