I have done a two day per week TGU routine in which one day was a volume day, doing reps OTM, for up to 40 minutes. The other day was the heavy day. I would start at reps on the 5 minute mark (OT5M). When I had a handle on that I would go to OT4M, OT3M, etc., until I could do the heavy bell OTM. It then became the volume bell, adding a couple of minutes here and there, working back up to 40 minutes. Meanwhile, I would bump up a bell on the heavy day, starting back over at OT5M.
I made at least as good TGU progress on that format as any other, so, naturally, I quit doing it.
You could adapt that to S&S, doing your ten TGU's at an interval that allowed good recovery, say OT3M for example, working to OTM, then bumping up a bell, or something along those lines.
I think you could be really missing out on some of the benefits of S&S by approaching it that way though. Learning to control your breathing and letting it guide your rests is worth doing. I resisted it for a long time, but finally made myself do it. Once I "got it," it was just another reminder that:
There is a very good reason for every single thing Pavel tells us to do. Every. Single. Thing.