This does not seem very easy. The triacs will be huge and you will have to worry about inductive kick from the motor damaging the triac junctions.
There was some discussion about arc welder controllers a few months ago. You can look through the archives. That discussion listed some part numbers. The devices were huge with large heatsinks.
I understand your frustration with mechanical contactors as the contacts wear out or weld shut. Their benefit is the size and the elimination of a heatsink requirement.