I can either switch the location of the sink / tub, or lift the tub up a bit and drain it into the main stack. I am not certain about the possibility of piping over to the drain pipe.
I don't think I understand what you are saying.
Here is what I think I would do. Maybe Mark has a better solution.
Cut a 3' X 3' piece of plywood. Put it in the corner over the tub drain hole, tight up against both walls. Sit the tub in place over the plywood. Make sure tub is tight against both walls. Draw an outline of the tub drain hole. Mark the edge of the tub on the plywood.
Remove the tub and plywood. Assemble and install the tub shoe, overflow pipe and tee connecting the two. Out in the opening, sit the tub on the plywood. Align side of the tube with the line on the plywood. Align the head of the tub with the edge of the plywood. Use a level to make sure the head of the tub is plumb with the edge of the plywood.
Mark where the drain pipe, out of the tee, would pass through the plywood. Make sure overflow pipe is plumb both directions.
Drill a hole just big enough for a pipe to pass through plywood.
Dry assemble trap with a short piece of pipe sticking out of the intake of the trap. Pipe should extend a few inches above the floor. Adjust trap so you can put plywood back in the corner with pipe passing through the hole.
Remove plywood and make witness marks on each fitting and the pipe so you can take things apart, glue and reassemble in the same position. Measure from center of tub overflow hole to floor. Assemble and install tub shoe, overflow and drain pipe to that measurement above the floor.
Carefully sit tub in place, connect drain flange and overflow cover.