I am sure that a lot of us forum users have looked at your submission and come up with a few ideas, but I am convinced that you must have looked into many of those already. So to err on the side of helping you, I will throw out a few ideas.
If the starter is turning over with adequate power then I must assume that you have a good battery (a new battery is best to eliminate this source of a problem)and good contacts that are giving enough power to the starter. A weak battery will not be any help in getting enough power to actually start a car. But of course it might allow the starter to make some noise. If the starter is spinning but the engine is not turning over there may be an issue with the distance of the starter from the flywheel. Could there have been or is there currently a spacer on the previous starter that changed the distance of the starter from the flywheel? The starter gear must move into position against the flywheel when the starter is activated. If the gear does not mesh with the flywheel there could be something wrong with the teeth on the flywheel or an incorrect distance from the starter to the flywheel.
Could this rebuilt engine have the wrong flywheel mounted?
I do not have a TR6, but is there an incorrect way of mounting the starter, ie, one particular side up?
Hope this helps you either find or eliminate a cause.
Charley
