“PAA, in fact the Gemorah says that R’Hillel needs forgiveness for what he said. It was not just stam an error”
That is an entire discussion in it’s own right. What did he need forgiveness for? Pashtus of the Gemara is that what he did wrong is that he went against the nevuah of Zecharia. The Gemara doesn’t mention anything about him violating an ikkur. If that is the case then it has no bearing on any other case where there is no explicit nevuah. If he needs forgiveness for the actual belief then that would disprove the psak thesis because R’ Hillel did nothing wrong if it hadn’t been paskened yet.