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I tried the upside down method and it works! But you will get foam rising up the seat tube and spilling out the BB shell, which will drip onto other areas of the frame and trash your paint. Lean the frame over a little from vertical so that the BB foam eruptions just hit the ground. Imagine you are dropping apples off the leaning tower of Pisa.
In any case, the "filling the seat tube" method requires a lot of fluid changes. Like 10 changes or more. And let's face it, anyone on this thread is game for some faff and shenanigans. But where possible I would just use the bath.
Wow, what a mess!
A variation on Ndeipi’s method: If you hang the frame upside down and plug the end of the seat tube with plasticine, you can pour your caustic soda in through the bottom bracket. That’s assuming the seat tube is open at the bottom bracket, which it usually is. You’ll have to hacksaw all those bits off flush first. That way you can do it without immersing the frame and you’ll be able to save the paint (probably not a concern here).