Just keep in mind it is better to drop your score now, than later on when you actually NEED credit.
Inquiry's drop off quick and AAoA bounces back. So, no matter what you choose to do, it won't hurt you too bad later on.
Though, sometimes it is better to have the best score possible when you apply. That way you get a higher limit and lower APR.
I would call the credit union back. That account really stands out on your credit report. Try to get the limit more in line with your other cards. Give them as high of an income as honestly possible. Generally, $36k is the magic number. Have you gotten a raise lately? Earning income any other ways?
Welcome to the forums be1991!
TLDR version: there's a number of positives for you to apply soon (mid-December), and really no negative in my opinion.
Rambling version: I'll offer a slightly different viewpoint than the others: if you want a particular tradeline, and you have a good chance of being approved (looks like you do for your BCP) it's best for your mid-term FICO to simply obtain it as soon as possible.
You already have a mortgage, and you already have a car, so I'm making the assumption you're not going to apply for anything big-ticket in the next year. As a result, as long as you can restrain yourself from constant applications () then there's really no downside to taking the shot sometime this year: in particular, once that Barclaycard posts it's sixth payment which probably means a December application for a BCP in my opinion. This is especially true as over the next 3-4 years Amex backdating (I'd recommend searching the forum for the term if it's unfamiliar) may well be a benefit to you at some point to have your membership date as 2012 instead of 2013.
When it comes right down to it, one's FICO score when you're not applying for something is completely irrelevant, and as long as you don't get sucked into constant applications, an additional inquiry, even if it's "wasted" (FWIW I don't consider a denial to be a straight waste) is on average 5 points or thereabouts, and sometimes no damage at all since you have multiple inquiries on your report already.
So for my math, there's good reasons to apply in December (no later than Dec 15th I'd recommend) and no significant reason not to. The card would absolutely be a non-trivial financial benefit as you suggest, you have a reasonable chance of approval, and it can possibly help you in the future to have your membership established this year rather than next. There's no real downside as your backup plan is to wait six or more months anyway from the sounds of it, by which time your current inquiries will have fallen off the scoring portion of the sheet, and your Amex one will be minimally impactful to your score, and presumably your subsequent Amex application if you're denied this time.
My thoughts anyway, longer term I think you'll be just fine with whatever you decide to do.