I have a suggestion, if not a definitive answer.
I have this engine, but have never had to replace the tires. I just looked at it and, yes, even if you "bottom-out" the driver, the screw seems to be trapped behind the crosshead guide lower "rail".
1 - e-mail Lionel; often they can help (if you get the right employee - it costs nothing, so go for it).
2 - it looks as if you can remove the main rod crank pin, then slide the main side rod, crosshead and piston rod back a bit (it looks like you can - you don't need much wiggle room), perhaps you can lift the #1 axle screw out between the crosshead guides so a new tire can be slid over the wheel and worked into place - this "working" is a whole other set of cussing opportunities, been there...done that...but that's just patience. Then put the screw back in.
3 - let's all get together and find the guy who decided that the most access-resistant wheels were where a maintenance item should be located, and just slap him.
4 - you can run the loco without some (or all) traction tires. When one of mine loses one, if performance is not affected, I sometimes ignore it. Totally case-by-case. If it's easy, I put one on right away. The 2 in the rear of your loco will probably be more than sufficient.
5 - I'm hoping that there is an obvious solution that I am just not seeing - like magic.