I independently arrived at the same method as the late great Mr Brown, with a slight variation. I didn't have a socket that would fit. So the solution I came up with was a nice long bolt with a tube as a sleeve on the bolt so I could get a spanner on both bolt ad nut to tighten it fully.
Once completely tightened it didn't take too much force to move the cup. Having said that I did use a five foot steel tube over the handle of my adjustable as a breaker bar! Since then I've always used this on fixed cups.
One important thing though, tighten the nut and bolt as hard as you can before attempting to remove the cup. If it's not tight enough it might slip suddenly and you don't want that to happen when you're leaning 13 stone on the spanner!
As for the heat method it's not particularly reliable. Better to apply a few well judged taps with special workshop tool #1 to the cup first. If there's something like rust "gluing" the components together this will break it. The heat method will work nicely on things like old grease, but it is unlikely to work well on rust. If you could heat the shell without heating the cup it might work, but that is very difficult without specialist equipment. I've worked in engineering shops where they have the kit to freeze one component while heating the other, but it would be fairly difficult to improvise at home.
Using your variation on the Sheldon Brown method, did you use something (or someone
) to secure / steady the frame? Good tip with the steel bar extension, I definitely couldn't get enough leverage with my measly 12" spanner to see any fixed cup movement, and by God I tried!