Andy,
You are correct.
So starting with the lock cylinder makes sense. Likely much easier than the linkage in between. Also guessing not a lot of money. (If it was $100 for maybe, that would be a different story.)
Likely it will fix or help fix the issue. (Buy you some time till the linkage wears out more.) If not the you only have one part more to buy.
Also if that does not work perfect, you can try to shim the actuator hole, guessing after 450k mi it’s wallowed out a bit. So maybe a little piece of rubber on one side. (So it pushes the ignition switch to the start position as much as possible.) It might buy you some time till you find a actuator arm. But likely the new switch and lock cylinder will take up enough slack that it will work.
Let us know how it turns out.