I'm afraid the elephant in the room is, a straight limbed, broom handle grip, longbow is not going to be as accurate as a recurve constructed to the same level of quality. That's why they have separate divisions for longbows and recurves. Everything you do to that longbow design to make it more like a recurve will increase it's accuracy: contoured grips, reflex deflex limbs, heavier mass weight. It is still a "longbow" as long as the string doesn't touch the limbs anywhere other than the nocks, but some longbow tournaments have stricter rules than that, so not all longbows can compete in all longbow tournaments.
This is not to say that a pure straight longbow in a shooting machine won't shoot as well as a recurve in a shooting machine, because it probably will. But everything you do to "soften up" that longbow is to make it shoot better in the hand, not in a shooting machine.
Personally, I prefer a highly reflexed deflexed longbow with a contoured grip to a recurve, because I think you get the best of both worlds: performance almost as good as a full recurve, and reliability almost as good as a straight limbed longbow.