You could find out if it's the engine or chain by when it shakes.
If it shakes at idle then it's the engine, but if it gets worse with speed, it may be the alignment with the chain.
I think the 505 has 3 spots where the motor mounts to the frame. Have you checked that you have good bushings in all of them?
You may want to make a plate that would tie all of the mounting points together, for both sides and use longer bolts to hold it there. Use cardboard to make a template, and cut it to the shape you would need.
The metal around the mounts may be fatigued and weak so no amount of welding will help. The only problem is, unless you have a buddy at a metal shop, it could get expensive