Usually any good quality grass hay is going to be fine. I would avoid grain hays like oat hay, because the carbs from the oat seed heads can cause problems for some sensitive rabbits. Also third cut grass hays can sometimes cause issues because they can be a very rich hay and not have enough indigestible fiber in them.
With your rabbit, likely possibilities for the sensitivity are that he was born with a genetic sensitivity, or that he acquired one due to other health complications. Intestinal parasites could still be a possible cause, and liver issues. So if the hay diet doesn't clear it up, treating for worms might be the next thing to consider. Then a blood test to check liver function. Though there is the possibility that this may not be cured and just managed with diet as much as possible.
I had two megacolon rabbits with extremely sensitive digestive tracts, and for this it wasn't curable but was managed as much as possible with diet. One was born with it, the other I believe acquired it after a severe bout with stasis or possibly due to coccidiosis. Both rabbits had to be on a very strict hay and limited greens diet to minimize their digestive issues and keep them as healthy as possible. And this did work for the most part, to keep their poop looking as normal as possible, for a megacolon bun.
The common food that always caused problems for them was anything with too much sugars and carbs. So they couldn't have pellets, fruit, carrots, etc. The one rabbit born with megacolon also had to have a very specific cut of hay or he would develop moist log shaped fecal poop. He needed a grass hay that wasn't too soft and was a mix of leaf and stalky stems. The hard stems are what provide a higher amount of indigestible fiber, which is what helped improve his digestive function and kept his poop looking more normal, and the leafy bits are what have the nutrients. So you need a mix of both for rabbits that are on a no pellet diet.
That's what I would suggest focusing on. Not the variety of grass hay, but the maturity of the cut. Too coarse of a hay and your rabbit won't be getting enough nutrients from the hay and will start losing weight. Too leafy of a hay and there won't be enough indigestible fiber to help improve gastric motility. So you want a good medium coarse hay with a mix of leaf and stem, with a fairly good green color and not sun bleached(inside the bale).