Since 1955 when Chevrolet put the 265 engine in, there has NEVER been a riveted-on motor mount bracket. There are two brackets BOLTED to the front of your 283, right beside the crankshaft pulley. The bolts have 9/16" heads. Unbolt them, and bolt them onto the 350 in exactly the same locations. The holes are there, as they have been on every Chevy V-8 that's ever been produced. One of the holes on the passenger's side will have a short bolt in it to prevent oil leaks from the fuel pump pushrod hole. Take that one out and replace it with one of the mount bracket bolts. If your 350 has a large-diameter harmonic balancer, it will be necessary to trim the brackets for clerarance, or just substitute the 283 harmonic balancer for the one on the 350. Either one will work.
At the back, the bellhousing for the 283 will be a direct bolt-in swap onto the 350.
Good luck!
Jerry