Well here's the idea I have for bringing the Excalibur into the development of the Edward Teller.
Immediately following the events in The Ultimate Computer, the Excalibur was surveyed and because of the extensive damage, was determined to be too expensive to repair. After any salvageable equipment was removed, the ship was to be stricken, and the hulk towed to a breakers yard.
Enter Fleet Dynamics, the shipbuilding firm pushing for the development of the Edward Teller. They had been hampered by the unease of some members of the Federation Council and Starfleet Command to go forward with the development and construction of what was primarily a warship and whose mere existence would certainly escalate tensions with the Klingon and Romulan Empires. As a result, practical tests of technologies that had been developed and tested in simulation, have been postponed numerous times, stalling the project.
Seizing on the opportunity provided by the weakening of the fleet following the M5 incident, Fleet Dynamics approaches Starfleet with a proposal to use the hulk of the Excalibur as a space frame to mount the new technologies and test them. At the end of the process the Excalibur would be returned to operational duty, all repairs and modifications would be completed at Fleet Dynamics expense.
Fleet Dynamics was a consortium of numerous companies involved in ship construction and maintenance with facilities all around Federation space. To sweeten the deal, they additionally offered to use their facilities to handle the repairs on the Lexington, Enterprise, Hood and Potemkin, easing the workload off of the already heavily burdened Starfleet facilities and speeding the process of returning those ships to duty. That was enough to convince most of Starfleet Command to endorse the plan, regaining the Excalibur was a bonus on top of that.
The Federation Council still had to approve the proposal and many members still had misgivings about the Edward Teller. After a disturbing presentation by Rear Admiral Rittenhouse highlighting the impact of losing 42% of the fleets Constitution class starships in the current political climate, the council gave their consent. Additionally, they unenthusiastically approved the construction of the Edward Teller, but only a single ship and only after successful testing of the new technology was completed and the Excalibur was returned to Starfleet.
Fleet Dynamics interest in the Excalibur was solely to move the Edward Teller project forward. Despite the Federation Council's reluctance, the directors felt that the ever escalating situation with the Klingons, Romulans, Orions and the Gorn, would eventually result in a contract for a fleet of Edward Teller class ships. Unofficially and very confidentially, they had been assured of such an eventuality by several members of Starfleet Command. So the refit of the Excalibur proceeded, testing of new technology was completed as quickly as possible so that work could proceed on the Edward Teller.
And speaking of the Excalibur, here's some new pics, changed a few parts to give it more of an in-between TOS and TMP look...