Charlie, photos and pics would be 100% helpful with your question.
if you don't want to re-frame the entire roof, consider putting a structural ridge underneath where existing ridge would be if there was one. i typically use a 2x on the flat (2x4 on a shallow pitch like you have) to go below existing ridge line, then add 2 or 3 lvl's spanning the length of your box. strap existing rafters together before you start jacking the ridge into final position, otherwise you'll just pop individual rafters. in this scenario you're able to leave existing mismatched layout.i'm redoing the roof on a 1940s war box house w/ 2x4 @ 2' o.c. rafters and ship lap sheathing on a 5/12 slope. i thought i was just doing the roofing then discovered the ship lap was rough so started tearing that off. now i've noticed that the rafters are not connected to any of the ceiling joists which are on a completely different lay out. and one section of the the front of the house notches in about 18" so with the roof line, the rafters don't sit on the wall top plate, instead there is a little 7" wall built on top of the top plate that the rafters sit on in that section. there is no connection to hold this little mickey mouse wall in so it is pushing out and the roof is sagging a few inches at the peak in this section... oh, and no ridge board, and no gussets on many of the rafters.
i'd prefer to reframe the entire roof with at least 2x6 rafters and the same 16" o.c. layout as the ceiling joists. but this likely wont happen. and even if i do, how should i secure the platform that the rafters push out on that is raised above the top plate? would running 2x4's across horizontally to the other rafter to mimic a truss system be sufficient? any other suggestions? pardon the pun, but this roof job is a little over my head...