I would end services with both. I would likely provide copies of all relevant documents (what I was required to have kept ONLY, nothing extra) to each, and prepare two more sets, one for each attorney to be sent as soon as I receive authorization from each party. This may keep me out of subpoena/court, which is an expense I may not be able to recover recover easily. Preparation at my timing may be better than under pressure of a court order.
If each knows the other will get the same set of required documents, it may reduce the need to involve me in any squabble. Depending on my requirements/restrictions, maybe I can ethically use the same letter to each, with a cc statement or something at the bottom.
I would make sure I was not in possession of anything I was not required to have. For instance, if I am required to keep 4 years of documents, I would rid anything more than 5 years old. (The extra year is to avoid any issue with calculating the time down to a day or month.) Documents I am not supposed to have cannot do me any harm...
The process should be exact, or close to, my process for firing a client.
Upon final dissolution, if asked, I might choose one to resume services for one. I would not entertain accepting either until final dissolution.