You should be able to sync into the existing T-Point model, but given that when using the automated platesolving mode it takes less than an hour for a full T-Point run, I would be inclined to redo the T-Point from scratch. Just wait for a night with thin cloud or full Moon thats no good for anything else. I find 1-2second images are easily deep enough. I just listen to music on headphones while manually rotating the slit to ensure the scope sees skies – the joys of a non-automated early Pulsar.
IF with an accurate time and an accurate position you still have issues it will help focus your attention a bit.
Just bought a second hand MX, but have not yet installed. Hopefully a lot better pointing than the NEQ6.