Howard,
I don't own a power jointer. I do my jointing and flattening by hand using an old Stanley Bedrock 607 and an old Stanley #8 which equate in size to the LN 07 and 08. It doesn't matter much which brand jointer plane you use, new or old, or whether it's wooden or metal, as long as it's tuned, sharpened, and set properly and you're using good technique, you can get good results.
Fran's description is a variant of what's called match planing. It is a very good technique and it works. Try it. I might also suggest setting up your clamps and dry clamping the pieces as you go along. Mark with arrows any gaps you see under slight clamping pressure and once the stock is back in the vise focus on those spots. Re-clamp, look and mark again, back to the vice for touch up then before you know it you're done. Sounds simple and it pretty much is. But, like anything, it takes practice. You'll get better.
Are you using your left hand (assuming you're a rightie) as your fence by pressing down on the sole near the toe with your thumb and dropping your fingers below to run along the face of the stock as a fence? If not, and your left hand is on the knob, then chances are good the plane is rocking a bit side to side when you push. This just about ensures you're putting little bevels right where you want it dead flat and true to the adjacent piece. The off hand-as-fence technique stabilizes the plane as you push by keeping it upright.
The edge planes are good tools at giving you a perfect 90 degree edge but don't excel at jointing because they are short. Along short runs they're good. But anything over 12" and I think you're taking a chance of putting a bow in there. Remember, you just need the adjoining pieces to be coplanar. If you use the match plane technique, it doesn't matter if they are a perfect 90 or not. Just coplanar.
Hope this helps.
Rick Yochim