I don't have advice to your specific question, but to the issue of tummy time in general.
My DD is now 7. We *thought* we'd done a lot of tummy time, but we learn now that her shoulder girdle is underdeveloped. She preferred to be on her back and we let her take the lead more often than not. This has led to challenges for her in fine motor skills, crossing the center line, and other phrases occupational therapists like to use.
The OTs tell us they are seeing a LOT of these problems in preschool kids now, with the push to avoid tummy sleeping for infants.
DS, 5, preferred his tummy. In fact, we could NOT get him to sleep any other way, no matter what contraption we used. He is having a much easier time in school.
So I just wanted to share the long view and tell you you are on the right track to make sure tummy time happens.