If I understand your issue, the lid is bumping the handles (which are leanding backwards) when you lift it ... if that's the case, it seems like you could just put a spacer board behind the faucets to bring them farther forward ... if you have 5" shanks, you should have plenty of shank to do that ...
To explain my idea better, you would remove the faucets, drill out a 1x3 or 1x4 (or whatever you want, perhaps 2x if required) so that the holes match the existing holes in the collar, and then fasten the spacer board to the collar with the holes aligned ... then reinstall the faucets ... of course, I left out the details, such as staining the board, perhaps beveling the edges, etc., but you get the idea ...
But in any case, I'd go with a different tap handle before I'd rebuild my collar!
Good luck!