I have this type of issue more with Chrome than Firefox though and it always seems to be related to leaving a tab open with a video for a long time, even if it isn't being played.
And the about:memory page, which shows you memory usage of all your extensions too.
Have you tried out the about:memory page? It doesn't do CPU, but it is a good way to see what particular pages are hogging memory.
As for why running the GC might increase RAM usage, I guess it is possible that some memory had been paged out, but running the GC causes the browser to touch all memory, paging it back in. That's just a guess though.
It seems to me that you could do this "well enough" if you put each page in its own process and let the OS tell you which are burning the CPU. There could/would be edge-cases where a page causing issues would not appear like it was causing issues, looking at it from that level, but it would sure as hell be a good start.