To address OP's specific question about SSRIs: One of the objective findings in people with depression is decreased REM latency (so you fall into REM faster), and increased total REM sleep. There can, of course, be other sleep disturbances such as insomnia or hypersomnia. But, all things being equal, a depressed person will spend more time in REM and less time in Stages 1-3.

All that is to say, decreased REM sleep from SSRI use may actually be normalizing your sleep cycles, rather than "disrupting" them. I'm not familiar enough with the literature to say that for certain, though.