Some time ago during one of the beta patches, there was another thread on this (or similar) topic where this guy managed to prove that AI HRE not letting people join empire if they have more provinces than emperor didnt work quite like that. Basically you could join empire with any country (that meets the conditions) no matter the size, all you had to do is spam the request. My understanding was also that AI would always decline you, but then i tried that myself, and boom joined France into HRE within couple of years. I have no idea if thats still bugged or not though.
I remember proving that with France and a screenshot....but I didn't spam the request...I held in the button and then released it...usually emperor always accepts then.