My thoughts:
Scavenger should be good, leave a Hunting Party on top that you didn't use this turn, and if somehow your Hunting Parties didn't leave everything in your discard pile, your Scavenger does that too.
Mystic would be bad, since it triggers a reshuffle of all your Hunting Party rejects.
Counterfeit isn't great, there's probably a better source of +buy, and your Hunting Parties ignore all that Copper anyway.
Dame Sylvia has a chance to hit your opponent's Hunting Parties, which is nice. If she's the top Knight, I'd say go for it - I doubt any other Knight combos with Hunting Party quite as well, and your opponent doesn't want more than one Knight because Hunting Party will trip over all of them.
All three of Counterfeit/Mystic/Dame Sylvia do have the problem of costing $5, which means you didn't buy a Hunting Party that turn.