Faced the same problem in the late '80s - playing county rugby, fit as a fiddle, blah blah. My challenge wasn't so severe as I'm a little over 5'10''. Pilot acceptance was conditional on the weight loss. Made myself ill (Cambridge diet, bin bag running etcetc) although I was so run down and caught every bug going, I was declared fit by the RAF!
Are they being 'weightist' in insisting you lose weight, irrespective of fitness level? Perhaps you could write to the current Chairman of the Services' Rugby union that you are hoping to join? Will you fit in the cockpit? Ultimately, you may have to challenge the jurrasic regulations through political/legal means, but firstly, just ask for common sense to be appplied.
Finally, don't pay any attention to the pie-eaters amongst us who have never attained your level of fitness, and now that they are serving, never will.....