Hi Andrew, lots of questions and I'm sure, as usual, there will be as many answers as there are members here!
Just one or two points from my own experience which may be of help.
Just to mention to start with, a tiny bit of play in stern tube bushes is not abnormal. The clearances even in a new tube can sometimes be more than you might expect so it may even be worth leaving well alone until you have run the model with grease on the thrust washers only and oil in the tube. If it seals and runs smoothly you may well decide to leave them alone. I do not use grease in the stern tube as, at the very least they will increase load on the motor and thereby battery duration, and at the worst they can cause too high a current in the motor. I grease only the thrust washers on the ends of the tubes and fill the tube with motor oil.
Replacement bushes can also be a little sloppy on the shaft as the machining quality can frequently leave a bit to be desired. Try them on the shaft first, if they are a nice close fit with little play but free to rotate they should seal reasonably well.
It is also worth considering ball bearings. These tend to be machined to much closer tolerances and should give a better seal but can again cause a little drag from the shields. You don't need to grease or oil the tube when using ball bearings for the sake of turning resistance but it is worth using some oil to prevent rust on the shaft. If the bearing isn't a tight fit you can smear a little bearing lock on the surfaces.
Take great care when removing the old bushes as they can be quite tight, especially if they have been in for many years, and the tube is actually very thin walled so can deform easily if you put too much stress on it.
I would definitely not be too quick to remove the old bushes before you have cleaned everything up, greased the thrust washers, put fresh oil in and tried it on the water first. You may be surprised that things are OK.
Also if the internal tube end and bush are actually above the water line then there should be very little reason for any ingress of water so it is well worth testing the model first.