To be honest, i don't understand how it works. Is your idea moving bitcoin transaction to side-chain or another blockchain entirely with custom script or tokenization?
OP is sounding like seeding an idea for on-going higher BTC tx fees. So, it can be side-chain or all new blockchain or anything; I guess it will be up to devs who feel which one is compatible and efficient.
I think there's already a thing like that you mentioned and it's called bitcoin cash except if I'm wrong.
Bitcoin cash? Then we have already such things at least in 100s.
OP, I like your idea. But, not sure about the feasibility in real time.
You sound like we need same bitcoins but on different blockchain. It may become possible if this will be possible: a trustless environment based 1 to 1 swap with backward compatibility.