Yeah there's a lot I don't understand about the proposal. Does it interoperate with vanilla tor nodes or is this a totally separate network? Are you paying each node on the onion route or just the end node? If it's just the end node, you are only incentivising tor exit nodes which is useful but I think a more general approach would enable paying routing nodes also.

With ecash you could literally include the ecash postage in each layer of the onion message. Each hop decrypts the next destination and the postage. Postage could be independently verified with DHKE and double spending prevented with p2pk locking. No extra network calls necessary. The tor node needs to trust the mint. Could be done with a whitelist like "I only accept postage from these mints."

For AMP or keysend on the tor network you don't have the capability to pay tor nodes along the onion route. Or if you do that is a separate lightning transaction for each hop. That would thoroughly destroy your latency, but I think LN's low payment reliability would be a bigger problem.

If it's a new network you could pay nodes along the route with standard lightning fees but now node operators have the additional burden of running a LN node on top of a tor node. That's a big lift for hobbyist node runners.