Scramblin', I had given some serious thought to doing just what you've suggested, but I've seen some awful examples of people in my situation (on the way up creditwise) who were denied for Capcard2, and took three Inq hits.
Then, there's the horrid customer services when the transposed numbers as the high limit. It was absolutely ridiculous, and at no time were they ever denying that it was an error, or that it was their fault. They just wouldn't fix it for the longest time, and they were horribly rude about it. the actual high limit was $483, and it somehow got reported as $843. They knew it was a mistake, and even went so far as to try to convince me that neither the high limit, nor the balance was reported to the credit bureaus.... while I was looking at my credit report and telling her exactly what was there. Another rep tried to tell me that it didn't matter, because it was Cap1's position that their customers shouldn't be seeking other credit because their products were so wonderful & awe inspiring. And, since they knew that it was an internal mistake, it wouldn't matter to anyone as long as I didn't seek credit from additional lenders!
Others outright lied to me and claimed to have fixed it, when they did absolutely nothing. It took months to fix, and they were horrible about it. This all started after my card was stolen in a restaurant, and they issued the new tradeline. There were no charges to the stolen card, as it was reported as stolen and cancelled within 10 minutes of having been stolen from the waiter. It was just something that Cap1 did in error, and couldn't be bothered to fix.
That actually burns me more than the lack of credit increase. I'll never get another one of their cards. And, after the scathing letter that I sent to get it fixed, they'd probably just as soon be rid of me too.