If the merchant is online, the customer just sends the ecash and the merchant swaps it with the mint. This is the standard flow, no issue at all. If the merchant is offline and the customer is online the customer can lock the ecash to the merchant's pubkey with a timeout clause. The merchant must get online, probably within a few days, to claim the coins. These are very reasonable constraints that can be broadly applied to real world commerce. I think it is fair to call this a half-offline payment solution.

If the customer can prepare ahead of time you can do a truly offline payment, but it requires the customer to lock some coins to the merchant's pubkey before they go offline. So the sender of ecash needs to know ahead of time who they are sending to and they have to set a spending max. If they don't spend it all the leftover ecash is locked until the TTL expires. So offline spending is technically possible but not really practical solution for most use cases. For this reason, I avoid the term offline payments.

Just for comparison, in order to make an on-chain payment the sender must be online at time of payment, the recipient must be online and connected to a full node to verify payment. To make a lightning payment the sender and receiver must both be online at the same time for the entire duration of the payment flow. So half-offline payments are a substantial improvement over the current state of the art.

As for your second point, you are correct, a mint can't offload their ecash promises to another mint non-interactively. This is fundamentally a privacy tradeoff. This kind of non-interactivity is not possible in a private system. So your issue is a fundamental limitation of privacy preserving tech.

An example solution that sacrifices privacy would be to associate each ecash token with a static payment address or a pubkey. You essentially have a mint account now which means they can track all of your ecash payments but the mint gains the capability to non-interactively close your account and pay to your BOLT12 or silent payment address. I think this is kind of what your proposal does, with some reputation or staking/slashing incentives.