Last night I was able to get most of the adhesive off. I did what I could with a knife and patience, then took a cup brush to it. It made a lot of nasty smoke and there are gummy rubber pieces about the size of a pinhead stuck to everything throughout my garage. Definitely do this outside if possible. All that's left is a very thin layer of adhesive smeared by the cup brush. A little bit of solvent on a scotchbrite should easily take care of it, then I'll treat the rust and coat it with something.
I'm sorry but that image of black splatter all over the place brought back memories that were both unpleasant and funny...I did the same thing myself and on top of the spray I also often found broken off wire brush pieces in my clothes that I would regularly discover rather painfully...
If you have invested in a 6 in 1, 9 in 1 or other tool they are immensely helpful to remove the factory coating on the frame before wire wheeling or whatever.
I used that tool for just about everything but managed to lose the 9 in 1 on a job somewhere and haven't replaced mine yet.
I would not try painting over it because with an older frame it has likely separated so there may be rust issues lurking underneath. I did often find patches of it that were sticking like they were welded on and that took a combination of elbow grease and sharp tools like a good metal chisel and hammer. The chisel is an excellent tool for framework and other things like removing scale (shale??) and other things that find their way onto the frame.
Once cleaned it is a good idea to follow your other project and hit it with rust converter and some epoxy or other sealer.
Problem I found was always thinking I could have gone a bit deeper with the cleaning...so I think I was a bit OCD with that when it came to my trucks...
Not a bad thing on any project but I always had to add time to everything for those "too clean" moments.