The approach involves using CheckTemplateVerify (CTV) or an alternative protocol simulating CTV to allow an update transaction to be spent via a settlement transaction that doesn't need a signature for each update. This is aimed at avoiding the conventional requirement where one party waits to receive another's signature before providing their own, which otherwise adds an extra step in the process.

To address the potential storage issue arising from the need to keep track of multiple historical update transactions and their corresponding settlement transactions, the programmer suggests leveraging the annex field of the update transaction. By doing so, it would be possible to recover the necessary information if an older update transaction is broadcast, thus eliminating the need for extensive storage.

An alternative solution presented involves using partial adaptor signatures for the update transaction. In this scenario, if Bob completes the signature, Alice can then reconstruct a valid signature to broadcast the settlement transaction. However, this method appears to complicate the spending of the update output in the settlement transaction as it may require dual signatures—one from Alice with a normal signature and another from Bob through the adaptor signature recovery. This added complexity placed the adaptor signature method into consideration but was ultimately deemed too challenging for the current scope of discussion.