Well, I would think you'd have to 'replace' the lost volume with something. Air, water, nitrogen, or crude oil come to mind. Air has obvious problems, nitrogen may not be available and causes some problems of its own, which leaves water and crude. I would think crude would be preferred. Having a small tank of oil would work, but there is probably the problem of where to put the tank? How about a diaphragm or bellows isolated surge vessel on the idea of a surge arrestor? Charge the dry side with a few psi of nitrogen. There may be some controls required to keep a back pressure on it while loading.

How do the big boys do it? Seems like heat or pressure are two ways.

CALM Buoy WLGP - Bluewater Offshore

What I would look for? Can't one extract crude with high vacuum pump. I would also look for ideas HERE

What will happen is that volatile materials within the fluid will evaporate to maintain their individual partial pressures within the pipeline at the temperature prevalent. So unless there is something that hasn't been disclosed to the forum, a full vacuum will never occur.

Put a heat exchanger at the turret and cool the crude with seawater

You may or may not need a purged line to start with. The equilibrium state will be partial vacuum due vapor pressure.

Once new hot crude is allowed into the pipe in preparation to transferring, full pressure is there, and transfer can commence.

No magic. What seems to be the problem to you, then?