Hello Niki,
You have a quite specific reason for wanting/needing a mover. this actually places you in a strong position as you must tell any potential supplier the detail of the job the mover must be able to do.
This is a very clear criteria, and the supplier must ensure that any product they recommend must be able to manoeuvre your caravan in the space and circumstances you have.
If you choose one of the recommended models, and have it fitted in accordance with the instructions, then you should be fine, But if for any reason the mover fails to meet the criteria you set, the dealer is responsible under the sale of goods act for not supplying goods fit for the specified purpose.
In reality, no one on this forum can make a certain recommendation as we cannot see the particular location and its difficulties. It makes more sense to go to the dealers and invite them to make recommendations.