I have a similar problem. Lacey has a trot that literally forces me to post. Like, I can try sitting it but after 5-10 strides, I find that my body, though still relaxed, is posting all by itself. That sound really weird but it happens. If I don't keep track of what my body's doing, I end up posting even if I don't want to!
Anyway, I'm not sure if these things actually correlate but as soon as I figured out how to post downhill, I started being able to sit her trot better. Now I can, sometimes, get a full 5 minute sitting trot.
I think it has a lot to do with me engaging and strengthening my core muscles. To post downhill you can't do it like you would going along the flat or up a hill. I think of it as "sticking my belly out" with each rise but there's really more to it. It involves staying over the horse's balance and using those core muscles in ways you never thought possible. It hard to explain but once you get it, you don't forget.
I've also found that when I try to sit the trot, sometimes I relax too much. I'm thinking "Stiffness makes this trot worse, I have to be loose!" but then I get a little too loose and my heels come up. If I keep my heels down/level (not stiffening my legs to get them down, just rotating my ankle to get them down) I have more success.
Of course, even now that I can kind of sit her trot, it's certainly not comfortable. I much prefer posting since sitting her trot makes me feel like I'm riding a jackhammer or a jumping bean.
Another thing to be sure of is that you aren't stiffening up in a response to the rough trot. That was an issue I had for a while, Lacey would start trotting and I would immediately stiffen up, trying to regain balance. I had to teach my body (through very short sitting trots) to automatically relax into the trot to regain my balance. It was really hard at first but now it's nearly second nature for me.
The plus side for us with our rough trotters is that after them, pretty much every other horse feels smooth. I've found that I can successfully, easily, sit every other trot that I've ridden since I really started riding Lacey 4 years ago. We can just look like riding pros and everybody will be jealous of our crazy skillz.