I built a "Franken" engine with a 1.6 turbo block, 1.5 rotating assembly, and a 1.9L AAZ head. It all bolts together, but you have to be careful, and you have to know what you are doing to have it work out properly.
The rotating assembly from the 1.5 has to be used as a set (crank, rods, and pistons) regardless of which block you use. You cannot mix and match cranks, rods and pistons between the 2 setups.
The heads are physically interchangeable. The rest is up to you.
If I was building for a daily driver, and I was in your position, I would rebuild it as a 1.6. You said you are going to have the block cleaned up (bored out, presumably). Oversized 1.6 pistons are easy to come by and comparatively cheap. Oversized 1.5 pistons are hard to come by and are expensive.
If you want more power than the 1.6, then switching to a 1.5 is going the wrong direction, in my opinion.
Steve.