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For me there is more the question why they gave you only a 1K limit? Looking at your siggy you already have a charge card with AX and other higher limit cards including CSP
This is interesting as I always thought the charge cards are easier to get than the revolvers. The only reason I could imagine is that this is a single large transaction so it got approved and if you had done hundreds of small ones they might have declined them over the limit...but this is just a lucky guess
If your internal limit with Amex is higher than your CL on that one card, Amex will allow you to go over your CL. The only consequence is your minimum payment due on the statement will be the normal calculated amount on the first $1,000, and the excess over $1,000. Thus, your payment due will include the $150 that exceeded your limit plus the 3% or so of the $1,000.
It possible to push a payment larger than what's due to AMEX via bank transfer or wire. If you know you have to make $3K in purchases you can always push a $2K payment before the transaction and you would be clear to charge the $3K no issues.
Also if you are moving that kind of purchases thru the low limit card you should not have an issue at 61 day CLI request. AMEX likes to see usage and PIF.
If you just use AMEXs website to do the payment your available credit will be reflected instantly then you can make the next transaction
no need to wait 2-3 days.
I have seen Amex let revolving credit cards go $1-$2k+ over the credit line... they can be a weird egg!