Faced with a similar problem, I eventually wrote a script that tracked where pieces are, and when a card has pieces, the script moves them separately to their correct places. It is tedious to track the pieces so carefully, but that's the way I found to deal with the problem.

Well, I've been playing around with this for a while. I've managed to make some improvements, but I'm running into a problem.

I added a grid, sized it to the cards (for the most part) and turned on snap. This makes the cards shift upwards by a quarter-card, so that the lines actually line up. On the GM layer (black), I've drawn some lines for reference. I included a bit of numbering so the host can easily tell how many cards to lay out.

I've put in character tokens from the included fantasy set, color-coded. This gives them a little something to do with their figure between turns (posing them, etc.). I've also thrown in jawa64's gold bar, because.

Now for the problem. TTS's physics do NOT like Timeline.

Every time I move a card that has any tokens or counters on them, they jump when I let go of the card, and scatter when the card lands. I've tried fiddling with various toggles, but I just can't seem to get those things to stick to the cards and behave.

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Colored wooden pieces are from the amazing Wodden Piece Pack https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=268153977