Hi
There use to be four class 73 locos used for maintenance/loco recovery. They were used for mainenance and recover. They were diesels, but could also operate from the third rail which they use to do in the loop. The last two left about ten years ago.
it does not help for the period that you are running, but the only occasional diesel on the loop is the Network Rail de icing/leaf cleaning DMU. It does not go right around the loop, but goes as far as the second platform at James St, sits there for a while and then goes back to the Wirral. They do run it during the day when passengers are there - have seen it at James St numerous times!
The Wrexham trains only go as far as Bidson and then return.
For the period you are modelling, there use to be a triangular junction just past Bidston station at the junction where the West Kirby and New Brighton lines join. Not sure when it was removed. if you look at arial photos, part of it still exists in the form of a small siding that the Wrexham train use to use to get clear from the main line befor returning to Wrexham. When the junction use to exist, it was possible to get a train directly from West Kirby to New Brighton without the train having to go through the loop first. Might give you a destination for your diesels?
The third platform at Birkenhead North (the one furthest from the station building) is used occasionally when there are operational issues.
If there are technical isses with a train from West Kirby or New Brighton, it is usually take into this platform to detrain the passengers who are then put on the next service to arrive on the second platform. The train can then be reversed down the track running beside the running line and taken into the depot for repair. Occasionally it happens the other way around with the train being taken out of service on the main platform and the other running through the third platform.
The other time that its used is when there are issues stopping trains running through the loop. They run a replacement bus services from Birkenhead North. Trains are brought into both the second and third platforms from West Kirby/New Brighton and emptied. They then pull forward towards Liverpool and then reverse back over the crossover into the platform by the station building before returning to West Kirby/New Brighton.