tires out of balance
no.. even though they are 31 inch tires...they should still not cause the steering wheel to vibrate. Here's the deal, every tire has a road force variant. In larger tires, this variant becomes more noticeable. Have your dealer (or who ever) do a road force balance. See if the road force variant is over 10. Getting into the double digits is bad. Anything in the single digits is very good. In smaller tires RFV can not be noticed as much.
Now in the OP message it is probably an out of balance issue seeing this is the first time he has experienced this issue with old tires. I had the same tires for 60k miles with no vibration issue what so ever. Bought new tires (same kind) and had vibration issues like mad. Finally convinced the dealer to road force balance all the tires he had until we found 4 with single digit RFV numbers. Smooth as glass again.