A frame with a frozen BB is unacceptable IMO. By not removing it now, you are simply delaying the inevitable. If your BB have the same structure as the BB-un55, it is made in such a way you will not be able to tap the axle out. Check out the BB-un55 structure in this thread
Repacking a Shimano BB-UN55
. These BB:s rely on grease to operate. Given the fact that heat has already been applied to the shell, the grease inside it may already be damaged. This will reduce the lifetime of the component.
My recommendation is to aggressively use heat, dont be gentle about it. Absolutely nuke it. Cool the component down with water before applying the tool, otherwise the teeth might distort. Consumer burners produce plenty of heat for this application:
https://www.hornbach.se/shop/Lodlamp...-detaljer.html
. Two burners at the same time is better than 1.
By following the BB-un55 instructions, you could disassemble the BB inside the frame. The end result would be that you can remove the axle, while the shell would still be inside the frame. I am not sure that helps your situation though.