Hi. I'm Dave,
I can try to assist you with this.
Please understand that a "tire pull" can be caused by EITHER tire - not just the one on the side it is pulling to. Try switching the front tires side-to side to see if this helps. Since you have already switched the right tire out with the spare, this eliminates the right tire. So if swapping the front tires makes a change, the tire that is now on the right (originally the left) would be the issue.
Tie rods rarely ever cause a "pull". In fact. I did wheel alignment for over 15 years and taught wheel alignment for about 7 years, and I do not recall EVER seeing a tie rod that caused a "pull" or "drift" unless it was badly corroded and would not turn correctly. You will not find that by checking your "toe-in", or looking for "looseness" in the tie rods. If a tie rod is causing it, about the only way to diagnose that is to disconnect the steering gear and swing the tires back and forth with them raised up so they can swing freely to check for any binding or sticking. In any case, this would be about one of the LAST things that I would suspect.
High resistance in the ball joints can also cause a pull. To diagnose a binding ball joint. Raise and support the vehicle and disconnect the tie rods from the steering knuckles and swing the steering knuckle back and forth to check for binding. Compare the effort required to swing one side with the effort required to swing the other side.
A "binding" or "sticking" brake caliper can also cause a severe pull. To check for this, raise and support the vehicle. Get in and start the engine and press HARD on the brake. Turn the engine off and get out and immediately rotate the front wheels. They should turn freely with little effort. If either of them are hard to turn (in this case, most likely the right side) the caliper slides, caliper piston, and front brake hose would be suspects.
Other than these things, you will likely have to get the vehicle onto a wheel alignment machine to check for high caster or camber angles, or an extreme "setback" or "thrust angle" condition.