ANYWAY in Lightning proto dev summit, someone pointed out that we might be able to have some kind of sign-only-once scheme that could be used here.
(also pointed out that the number of bonds have to be equal to the number of clients; so for example, for a 2-client leaf, the LSP can allocate 1/3 of its funds in the leaf while only one client is online; more generally, for an N-client leaf, the LSP can allocate 1/(N+1) of its funds if only one client is online).
The following pointer was given regarding possible constructions that might be workable for sign-only-once today without OP_CAT: Bitcoin Clique: Channel-free Off-chain Payments using Two-Shot Adaptor Signatures