I'd also vote for installing a separate starter button. Well over 10 years ago, the ignition switch on my CJ7 failed so that it would work in the ACC and OfF and RUN positions, but it wouldn't work in the START position. So I purchased a starter button switch for a couple of bucks, wired one side of it to a fused, constant-hot 12-volt source, and the other side of it to the starter solenoid.

Works fine. When I start the Jeep, I just turn the ignition switch to RUN and then momentarily press the new starter button to engage the starter.

This even has an advantage. If I leave the ignition switch in the OFF position and then press the starter button, I can use the starter to "bump" the engine around without worrying about it starting.