Stuck GXP Bottom Bracket

Hullo Fine ladies and germs of the forum.

Now I've taken this one off and re-applied a couple of times, but now I seem to have gone full moron and am incapable of removing the goddamned thing. Seriously....I've snapped two allen keys as it is. The tool I'm using is this: http://www.evanscycles.com/products/ice-toolz/hollowtech-ii-crank-adaptor-tool-ec007565 which while tough, it doesn't really hug the whole cup.

Anyone got any ideas? To begin with, I've got the bike upside down, and I'm un-threading anti clockwise on the drive side and vise versa on the non drive side. Anyone have trouble with one before?
I don't have a bike stand or a vice to attach the whole cup to. I'd really like to take this thing off. Ideas welcome.

Your unscrewing strategy sounds correct. Some BBs have arrows.

This tool looks more promising as it is deeper and square drive:

http://www.wiggle.co.uk/park-tools-hollowtech-ii-bottom-bracket-tool/

You could probably destructively remove it with a pipe wrench of some sort:

Where are you?

I'll try to give it a shot, though now I'm thinking it's the lack of adequate leverage that's hindering the removal (and the tough seized bastard). I think I might have to go down the destructo route with the pipe wrench! Sigh...

I'm located in Marylebone.

try a park tool bbt9

try a park tool bbt9

I would, but I can't justify buying two tools that do the same job on a BB system I might stop using. I'll ask around.

Could you use someones' bench vice?

I will take it out for you. I am in W10 6ET

I will take it out for you. I am in W10 6ET

Thank you so much for the offer! I've ordered a new BB so just waiting for it to arrive (It's my work bike, so I can't keep it off the road for too long, alas, that means continuing the use of this BB).

Amid my reading (I'm hoping this might come in handy for other people) I kept noticing that no matter how much adjusting/tightening/cleaning of said BB, there always seemed to be a tiny amount of play, which gradually got worse. Not a lateral play, but rather an up and down by a couple of mm. This had a detrimental effect on the BB and over time, a noticeable creak of taught metal happened with every revolution, specifically on the non-drive side.
I found this by accident: http://www.the-climb.net/2011/09/truvative-bottom-gxp-bottom-brackets.html

Over time, it seems like all that play really beds in the BB cups into the threading on the frame, which might explain why after about a year, I can't explain why it's harder to remove the BB.
Is it worth spending the extra on a higher end BB? Or does it make more sense to just get another throw away. Maybe riding fixed damages the BB quicker due to concentrated forces? (I'm sure this can be refuted easily by someone more knowledgeable then myself).

Oh well, I just hope no damage was caused to the frame.