Thanks for sharing your thoughts and suggestions Murch! I’ve noted three concrete things I can try from your reply. I will work to produce some simulation results that can test these ideas.
One additional idea I’m exploring is to take advantage of an addition degree of freedom unique to Lightning funding transactions: we do not need to hit the exact amount requested. Any value over (or under) the target funding amount will do when funding a channel. The funder still controls the funding amount in the Lightning channel and can charge for the exact amount added.
When doing coin selection for BnB the excess amount is considered waste, but we can add it to the target amount instead of letting it go to fees. If one of your bucketed UTXOs is a little to big or small (eg. within 5%) it should be possible to use it for a changeless funding tx without any waste.
I’m testing out this idea now in simulations to see what impact it has on total fees.