Before you mount the Bontrager's or any other tire on the Arayas, check the bead on the inside of the rim. Is it a hook, a buldge or is it flat, relying on gum wall and steel bead of the tire to keep them on the rim. If the inside of the Arayas are flat/smooth, maybe you want to just leave the tires that are on there already. If you've got a hook bead or buldge, then I don't see why the 1 1/8 tires won't fit. I've done it with no problem.
As for finding narrow 27" rims, as has been said, they're not common. I have a set that came with my 87 Nishiki Custom Sport. I'm building another set from two narrow front wheels that I found over the last two years, one an Araya and one is a Rigida. I'm converting the Rigida to a rear wheel with a hub and spokes from another damaged 27 inch rim so that I'll have a set.
If you can convert the frame to 700C, you can accomplish your goal much faster as old, freewheel hub 700C are not as hard to find.