Ok scrap that! But I think tinkering with player GS is better than Team enthusiasm.
It might be interesting to do it the HT way, with the possibility of an Enthusiasm hit upon transfer. (New Player got a bad start with the team, enthusiasm drops 1). It would be a bit of a gamble, which always makes things more interesting. Add a 1 GS demotion to player automatically, and a (x)% chance of enth hit. If you lower the TL prices of these players because of changes, it also adds a bit of gamble to renters. Declining values means eventually someone will get stuck with a player no one wants on the TL for fear of getting stuck with the hot potato. The less use for these players in the BB world, the less of them will appear.