The spring clips are made for 5/8" drywall thickness, max. If you can pull some of the flooring above, you can fit new work cans. Or maybe a remodeling can is made for thicker ceilings, but I never ran across those.

Casey

Can lights are really out of place in an older home.

Why not just put in 3 or 4 bulb semi flush mount fixtures? And then provide additional light with floor or table lamps? It's not like most people typically use overhead lights in a bedroom much anyways except when cleaning or looking for lost car keys.

The work to award ratio, and chance for damage are really not in favor of this project.

If you really want the look of recessed cans, consider some of the new slim LED fixtures, such as Philips SlimSurface LEDs. They look almost identical to cans, but require only a regular J-box. As a consequence, they are much easier to air seal, and require a smaller hole in the ceiling.