There's a saying I adhere to, it's kind of a joke, but it rings true quite often : "when in doubt, rip it out".
In my experience that means to get back to original conditions and then proceed according to established construction practice for the best results. You can spend hours/days/weeks scheming a way to accomplish your goal in an alternative manner, or you can rent a jackhammer and start busting up the slab
Of course, I am approaching this as a professional and so substandard results are not acceptable (no offense diy'ers!).
Another way of looking at it when you get bogged down in a construction project, what is the Critical Path?
Remove slab, form new slab, pour new slab, finish new slab
This would be a two day job for my concrete sub.