Depending on the tire...I've sometimes taken the tire and, using a piece of brass rod for the gear strut, pressed it against the bottom of a pan full of boiling water. Sometimes it works, sometimes it doesn't.
You can flat-spot the tire, then add some filler putty to the sidewalls to replicate the bulge. Let it harden, then shape it with wet-or-dry paper.
Jeff Herne
PS: Very nice F4F, those panel lines look great. The presentation is very nicely done with the carrier deck as well...wow...it's taken me a long time to get where you are just starting out...