first try Firefox 3.6.15 and enable Value 1
that should fix the problem in Firefox for "I am trying to achieve is seeing the same colours in PS as the ones I get in web browsers."
if it doesn't then something else is going on and you may want to get a good reference image like the sRGB PDI color image
you also may want to review the other Adobe threads on wide gamut monitors and the difference between sRGB (web standard) and adobeRGB (your generic monitor space)...including bad-defective monitor profiling packages (and how to rule out the monitor profile)
i would recommend setting Ps Color Management Policies> RGB to Preserve Embedded Profiles --- a good way to achieve that is to first set North America Prepress 2, then change your working spaces, then Save (with no other messing around)
Ps "Assign Profile": The ONLY time that move is correct in Ps is if your file is untagged and it is based on sRGB color space - all other times you will first Use the correct profile then CONVERT to sRGB (if not already there)...
I don't really care about the colours in PS being incorrect for print, etc, as I am a web designer and the only thing that matters to me is monitor colour.
photoshop prints through a Source Profile> Print Profile CONVERSION
your monitor profile has nothing to do with how Ps prints your source color
(at least in my work flow)
photoshop displays RGB color through a Source Profile> Monitor Profile CONVERSION
your print profile has nothing to do with how Ps displays your source color
after you get your monitor profile ruled out,
the next step is to verify if Ps is using the correct Source Profile, and if you are Saving your web images in sRGB, and if you are embedding the sRGB profile or not
the last step would be to nail down if your test browser reads embedded profiles (it is color managed like Ps)
and what profile the browser applies by Default (in the case it is not color managed, or the test files are untagged)
and if that Default profile is then CONVERTED to Monitor RGB or sent straight to the monitor...