I have burned CRP, primarily brome, many times, but I can't say that I have immediately reseeded right after the fire. I do find that by just doing a burn that the resulting regrowth will include other plants, that were obviously in the soil all along, besides the brome. So I have gained some plant diversity by doing nothing other than burning and then letting nature take its course. It seems like that helps for about 2-3 years and then voila...the brome starts dominating again.
That being said...I think Jordan is probably right above, in that brome or fescue would tend to dominate other plants seeded just following a fire. So.....how about going ahead with the fire, then wait 1-2 weeks until the new brome/fescue starts growing back and then hitting it hard with gly and then broadcast your other seeds? I know you can get a smoking good kill on "fresh" brome by burning, waiting for some regrowth and then spraying.
And if you time it right, you would still have plenty of bare soil for your preferred seed to "find" and the brome will have taken a major hit...and you should still catch plenty of spring rains on your new seed, etc.