So you have someone doing the engine, finding a prop shop for the prop.
Who is removing/refitting the engine and prop?
A third entity?
This is a job I would stay well away from - best find a RMO, let your assessor know that's the one you want.
Then leave it all up to the RMO and the assessor to rectify it.
What will happen if after installation there is a defect with the engine or prop, say an oil leak on the crankcase that requires removal again?
If you arrange it the engine shop says fine we will fix the leak for free, just send the engine back. You can be up for removal/install costs and freight if applicable.
If the RMO arranges it even with your preferred engine shop, they will have a mark up that will cover this event and it is very clear where you go to get it fixed - the RMO.