Anchoring an SPV light client on another chain: checkpoint trust, retargeting and reorg handling

I think in practice you can check that the bits is above the lowest bits value of, say, the year 2022, which is hardcoded in your callee, and keep this simpler stateless design. Statelessness is next to godliness. Every four years, change this bits minimum value according to measured samples of the Bitcoin blockchain.

Alternately if you really really really do not want to have this simple heuristic solution, you just need to agree on some canonical header chain from genesis, without having to validate actual blocks.

I think it should depend on value of the amount in question. Your bounds should probably be something like: 100 if it is at or above the minimum coinbase amount, 6 if it is near to a typical Lightning channel, then just scale between those somehow, maybe logarithmically.