This, exactly.As a DM, you sometimes need to add rules to the game when the players step outside the expected rules. If PCs were doing this in my game, I'd have the extra heads wither away after a few hours, for example. There is no reason to have this in place for a monster description that is expected to be slain when first met - but it makes sense for it to be there now as otherwise there would by hydras biting their heads off to become unstoppable like this somewhere along the line.
OP, your buddy is bending the D&D rules to the point of absurdity. This is where you need to step in and say, "Sorry, hydras don't work that way. You can't grow a thousand-plus heads." Put some kind of reasonable limit in place and stick to it. If your buddy has a problem with that, then the problem is on his side, not yours. A DM must be able to say no to the players.
(And I would have a real problem with the jokes. Maybe once is funny, but repeatedly... not cool. Have you actually asked your wife how she felt about that?)