I can bend the headtube around into alignment and force the rear triangle in to position but its likely to show in the tubes.
Nearly ever Schwinn lightweight I've ever put on the bench has had a twisted headtube, which makes the front wheel lean left and the rear wheel to the right a bit when riding but the difference is very slight. Usually you can see this just buy looking down across the bare frame lining the headtube up with the seat tube.
I've had a few Varsity 10 speeds, mostly in larger frames, that road terrible because of it but mostly because they would turn harder to one side then the other, but only enough where you noticed it when riding hands free.
I would bend them back into perfect alignment and make the bike feel so much better. I just did a 65 Racer for a guy who was getting ready to do a repaint. It was only off about 1.4 degrees but perfect is always better if its possible.
Some of the older bikes just were never built to this sort of perfection, and they really didn't need to be. Most were built in jigs either by hand on a frame assembly machine. Its highly likely that a few just aren't set into the jig perfectly and get misaligned from time to time, maybe even most of them. They likely just rack them into 'good enough' shape and build the bike. They weren't precision watches, just kids toys to most back then.
I've got a junk ladies JC Higgins in the shed outback, it was my backup bike in the 60's for my newspaper route. It was hit by car before I got it, the fork is off an old Colson, I straightened it back then with a 5 lb sledge hammer and a torch. The forks are forged, the originals were tubular), but one got bent outward one day when my brother borrowed it, he got a flat, didn't tighten the front wheel enough, and the left side slid out of the drops, when he landed, the wheel came back, then the bike went over bending the tip of the fork in a 90 degree bend outward on one side. I heated it up, hammered it back in place as best I could and since that side was now a bit shorter, I filed out the left dropout a bit more to center the wheel The fender was trashed so it never went back on. The bars are welded because the stem bolt broke off, they were also straightened and one side was cut off and a left side was welded back in with a piece of water pipe for a sleeve.
Its got two different rims, the front wheel is an old Lobdell rim that's been brush painted green, the frame was painted red with a brush long before I got it and its faded to pink, and the back wheel is off a newer Huffy cruiser with an old Allstate tire. the back fender is off a rusty old Workman warehouse bike and is painted black with a rattle can to stop the rust. Its got a pair of saddle baskets and a huge front basket. Its still got its orignal slip link chain, made to work by welding an old ND sprocket with the center torched out over the Shimano rear sprocket.
In other words its a total mess, but it rides just fine, the bearings are all good, it don't pull and it stops most of the time if your lucky. The tires even hold air for almost a full day. My dad pulled it out of a dumpster somewhere in NY state while driving a truck one day back around 1967 or so. We beat it half to death a dozen times as kids and its been to the bottom of the swimming hole more than a dozen times, jumped off every ramp like thing we ever found, including the fallen down roof of an old chicken coop that used to be back in the woods then, it was like a long asphalt roller coaster ride that ended in a 15ft flying leap into a trail through about 20ft or so of fine sugar sand. A lot of bikes died there, I welded a lot of frames back together too back in the day. It was before BMX so we beat up the old bikes that we got cheap then.
So when I get on this Columbia and its so bad, but really don't look all that bad or out of shape, it makes me want to figure it out more.
The thought about one fork blade being too far back is spot on, that will cause a pull, but this fork is good. In facts I've tweaked it into perfection o the FT-4.
What I'm thinking is that since the rear wheel sits off to one side, the pull is partially coming from the rear of the bike trying to effectively turn to the right while the front wheel faces inline with the frame, the turn right is thus changing the center line of the bike then making the angle of the headtube wrong in relationship to the direction the rear wheel is pointed. Thus the more weight, the greater the caster effect.
What I think I'm going to try is to pull the rear over till the wheel, which I'll redish as it should be, faces the center line of the bike.
In other words, buy forcing the upper triangle over to match the chainstays to force the rear wheel to align property regardless of the funky weld to the upper frame, it should force the front wheel which since it can steer, to not try and roll to the right. It should put the head tube in line with the rear axle on all planes reagardless of where or how miswelded the head tube is.