I had the same problem for many years, yet I was determined not to go back to shooting a recurve.
So. . . I kept buying one to two or three high-dollar longbows every year, trying to find a longbow that I could shoot as well as a recurve, any recurve.
Finally, almost as an accident, as I had been led to believe they were the worst of the worst of all the longbows, I tried a Howard Hill longbow.
BINGO! Dead tight groups again, just like with a recurve. I was not prepared for that, but it was repeatable, over and over and over.
I cannot decide if the repeatable accuracy is due to the straight grip, or the lack of deflex (Hill bows have reflex, but no deflex), but it's one of the two, or both, that make Hill bows, for me, shoot just as accurately as a recurve. I have not been able to do that with any other style of longbow.