The hinge is held in place with a pin under the dash. Parts under the dash need to be removed to get to it. I don't think you need to do that. There is no adjustment from that end.
When the hood is closed, is it flush around all edges? Is the gap constant around all edges?
When you close the hood, does the latch hold it in place easily or does the latch pull the hood down, right or left before clicking into place?
Hood alinement adjustments are done where the two hinges bolt to the hood and the striker pin/base plate.
Getting the hood flush with the shroud are done with the rubber bushes. They are held in place with a split rivet. You'll need to figure out where to drill the hole in the rubber bush for the rivet's height. Too low it doesn't touch the hood. Too high and the hood will not close right. You want just a little pressure so it doesn't move.
Once all those things are addressed, the hood should centered and not move at all.
If you made changes, you may have to adjust the hood release position at the hood latch slider.
Lot's of tweaks/adjustments that will eat up a lot of time. Persistence and patience. But as a Healey owner, you already know that.
