I've had a chance to run the game now. I posted the Actual Play in the appropriate forum.

One thing I tried out in the game was a modified conflict card mechanic that eliminated the need for the card wheels. The only major rules change is that wild cards can't be used for escalation:

Escalation: A higher card in the current suit. No wild cards.

Change Style: Two cards in the new suits, or a card and a wild card, to change suit. The low card is kept, the high card is discarded. The wild card is always considered "high".

Cancellation: An exact match of the last card played, or a wild card. Discard the card played, take the opponent's matched card and steal one card from the opponent's hand. This is basically the tip on p. 73.

These rules changes means that in all situations where wild cards can be used, the wild card is discarded, and only cards of the appropriate rank and suit remain in play. Therefore, there is no need to remember or record the value of a wild card.