Not that I am trying to disagree with what you said because I don’t, but I wonder how “eilu v’eilu” applies to their machlokes. Also, the machlokes itself seems weird to me because it seems as they are arguing in the metzius. Either moshiach came or he didn’t.
This gemara is first brought on the amud before (98b). The gemara on the amud before (98a) says that R’ Yehoshua ben Levi even went up to shamayim to ask moshiach when he will come.
I don’t understand how this works out. Did someone leave R’ Hillel out of the loop about the heichal of Moshaich?