there is more than just "a bit" of modding needed - this is serious fab work. you are talking about all new custom mounts front and rear and lining everything up and making the mounts out of metal - if you are not used to doing motorcycle frame work this is a big project.
Matt, running 360 motors are a dime a dozen - what's wrong with just buying a good motor and dropping it into your frame to get your bike back on the road?
the 350 doesn't just have a good engine aftermarket, it has a good chassis aftermarket too which you would be loosing out on if you used the 360 frame. to me there is not enough good qualities about the 360 frame to do all the work to stuff a 350 in it. If you want a 350 go buy a 350 - if you want to work on your 360, work on getting it running again.
if you really want to do the custom work to put in a different engine, then pick a bigger or more modern powerplant like a cb450 motor or an ex500 motor (or gs500). If they fit the frame dimensions then it is the same amount of work as putting a 350 mill in the cradle. A two stroke dirt bike powerplant would be cool too and hella fast (kx250, CR250, YZ 250 etc...), this would be the way I would go.