One of the cashu.me (or npub.cash) superdevs should take the cashu.me option one step farther and forward the actual ecash token to the user as a DM. Then the wallet could pull that with a key signer extension.
I think the “claiming” on a third party site is too much to remember. I do like the npub.cash style where it is stupid easy, if it would just forward to my DM then a client wallet could incorporate these automatically.