I've had a bike I built for a friend do this and got around it.

First off if you loosen the main body of the BB a turn or two can the other side now be pushed over to center? If so the outer face is off and is wedging the BB to be crooked. This is by far the more common malady rather than the threading being off center.

Assuming it is the lip that is levering the body over there's three ways you can go. First is to leave the main body a little loose until you get the new plastic ring into place and only then tighten up the main body but don't over do it. Just enough to lock it firmly without overstressing the rather small contact point and threading. This isn't the best option for a regular commuter since there's a risk it'll work loose. Second is to have a shop with the right facing tools cut the facing so it's square with the threading. Third is the cheapo in between way that requires a bit of skill and judgement but will get you by if you can aim a file with good results. And that is to note the contact point and then file the edge of the shell down yourself to get rid of the contact point. This last one is the option I used on a rescued bike I fixed up cheaplike for a friend to allow them to join me for rides. If you do this it's not bad. Work the first high point down a bit and a little to either side. Run a ring of felt marker around and screw the BB in and with the wrench work the tightening point back and forth a bit. Remove and file down the new wear marks in the marker ink. Remarker it and screw the BB in again... etc... etc....etc After a while you'll have worked it down enough that the BB sits on quite a few spots and the other side is centered enough to let the plastic ring fit into place easily. At that point one last cleaning of the threads to remove any file dust, grease everything up install the BB and plastic bushing. Then sit back, rest your arms and smile at your command of old world machinist skills