Two things always bugged me about Give or Keep: you weren’t actually “giving away” anything, and the “keep more than you give away” mechanic rewarded greed.
So, how about this:
Choose a partner for the stage player (either a second person from the audience or a home player). Now flip the script: for each pair, try to choose the more expensive item *to give away.* Your partner gets whatever you choose. If you give away more than you keep, you win the bonus and get to keep the prizes you choose for yourself. Sure, you can be a punk and keep the more expensive prizes for yourself, but you don’t get the bonus if you do.