
Frank,
I have a 59 TR3 with steel wheels, and have the same problem as you, the radial on the rim at full pressure won't fit (neither did the bias ply tire.) What worked for us was to drop the pressure in the spare until it will slide in the compartment and then lock it in place with the strap. Before you take it on an outing, FIRST, go to one of the discount stores and get an electric air pump and a carry bag. If you have strong arms and back to match, a manual pump will work. The electric pump power leads can either be clamped on the battery posts or get an 12 volt accessory receptical and plug it in to that. I also got a scissors jack (like the TR4 variety) and another carry bag. This makes it easier to lift the car off the ground the flat tire fairy strike us on the road again. (Since these precautions, I have not had to use either) If you are showing your car in concours competition, you can just take the bags out of the boot and stow it with the cleaning supplies and other non-concours equipment you might have stowed there.
I wish I would have had known about these items before the TRA in Branson. The bias ply spare didn't fit well in the compartment either. It was so low that it wouldn't support the car. I don't know if any one else has used this approach, but I read about it in one of the sports car publications. I'm for anything that will make my life easier maintaining my little British car.
