Ok, I take your word for it here on tracking the UTXOs but the second part kinda contradicts your OP where you said the mixer would be a maker. Are you going to run takers too, or just produce a client and expect others to run it?
The Maker and Taker code would be written from scratch. However, still interfacing and communicating with same IRC channels as the regular JoinMarket Python software. Transactions produced would still appear as if they had been produced from the Python software. I would not be running on an entirely different network, but the internals and decision making in terms of which UTXOs were selected and which Output Addresses I chose would be up to my own software.
You said it yourself - CoinJoin doesn't break the TX graph. So I don't think you can also claim that I'll never get my previously deposited coins and it's incorrect to say this:
The user would get the best of both worlds so to speak, they would jump the transaction graph
Strictly speaking, 1 CoinJoin away, I think you're definitely right. Sorry for that, but at what point does this change? I am not sure this is "absolute" as it dilutes to some extent with time?
If you sent Coins to an Entity which then performed 20 CoinJoins in a row over time. If you received Coins back from that later, are these still "Your Coins"?