If the 1.6 engine is free and working, and you're willing to do the work yourself so that it doesn't cost you much, why not try it.
Get the engine, gearbox, loom, manifold.
Replace the clutch as you put it in.
Get a set of Mk2 GTI brakes as they'll fit your Mk2 better and the Mk1 brakes were pants anyway.
If you go down the Mk2 GTI donor route, then you'll probably want to just strip out the engine bay and dash of your Mk2 1.3, then you can just transfer everything across including the entire wiring loom and clocks into the dash.
Find a crashed donor Mk2 GTI, something that's got rear damage so that the engine, driveshafts and even steering can be transferred.