I'm surprised they weren't willing to compromise on the alone time issue. That seems like it would be rough on them in some ways -- who doesn't like to cuddle and bond after sex? -- but it's sure as hell better then letting you get to the point where you are damaging your health and have to choose between setting an ultimatum that they stop altogether or else break up with your bf. Especially since, at least the way you framed it here, it would be a temporary measure.
Do they understand how serious this is for you and what the stakes are?
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.