I fail to see the "private blockchain" aspect of what you are describing above. What's the difference to colored coin / token approaches such as OMNI and XCP?
I would like to gather better technical description for it.
I've researched about `SIGHASH_NOINPUT`and schnorr MuSig (n-of-n). Which will make it possible that all participants (owners) have a say in Merkle tree generated. With a small transaction.
And this Merkle tree will be used in a specific way which makes it possible for private blockchains to track and verify new blocks of those blockchains.