It's possible what follows contains logical mistakes.

I was toying with a similar idea where each output would be its own Utreexo. Since that's a forest of trees, an output would need to keep the roots and each root would have the amount sum of the elements in the tree. This way, we'd know the amount the Utreexo UTXO holds and can do the inflation check.
Much like Utreexo, a transaction comes with is a list of inclusion proofs [proof1, proof2,...] which gives us the inputs. A transaction also defines the outputs that are created. We check the signature and that the transaction is well balanced and then delete the inputs from the Utreexo tree and add outputs as new elements to the Utreexo.
I'm not sure I remember correctly, but I believe anyone can delete an element if they have the forest roots and the inclusion proof and anyone can add an element if they have the element and the roots. Since we have both as part of a transaction validation, anyone can update the Utreexo accumulator.

This obviously isn't compatible with Bitcoin today, but may be an interesting direction to think in. Those interested in a specific Utreexo may have the tree saved locally and could share it with others in the tree if someone lost their inclusion proofs.