The only other solution that I support for the headaches bids have caused is that instead of being scored at the end of the game, they get scored at the beginning. Make it an actual bid as in wager . You can put up the points to get the advantage, but your opponent starts that much ahead. This would get rid of the 'invisible upgrade' that the bid currently is.
The cap just sounds easier and maybe a bit more interesting of a head game.
Edited by ForceSensitiveFrimmel ninjad me while typing lol