I think the bidding mechanism is basically sound.
Every player gets a range of tokens in a variety of colours from a limited pool. They offer their to tokens for the right to address the pilgrim. All tokens go into a central pool once the bidding is complete, then they are evened out and passed back.
If everyone has 3 tokens of 3 colours (9 total)
Player A bids 6 tokens (left with 3), Player B bids 4 tokens (left with 5), Player C bids 2 tokens (left with 7).
Once the bidding is complete, 4 tokens are distributed back to each player (A ends up with 7, B with 9, C with 11).
In this way the tokens fluctuate around the group, players might choose to play strategically, offering a low number of tokens for the chance to build up...then launching a massive bid when they see a pilgrim they really want to interact with.
I'm now thinking of a single bidding phase for each pilgrim, because a bid for each question is slowing things down in the test runs I've done so far.
It's getting late, time for sleep. Maybe I'll think fresh in the morning.
15 hours ago