Had the BCP for a year now, and 2 CLI already. They like it when you run serious money through it. Because it's my go-to card, I let it report 1-9% every month, and have the other cards report 0%. I think this is the best strategy. Also, make sure you check your score, so that there are no surprises.
remember Amex is originally a charge card company they don't like large balance carry overs, but with that said a under 15% is perfectly fine, but I would keep it at 2% which is known as the magic number for your credit scores =P
Regardless of the amounts, ideally will have as few accounts as possible reporting any balance for best results.
2.5k is not an insignificant balance reporting on one account (is it more than 50% of CL for e.g.) particularly as a student unless income/ payment history is exceptional/ better than average. Big limits beget big limits but without the personal income to support them, such requests can become dicey on a typical full time student income.
The lower the balance reported, the better. Probably less than 10% CL is a no problemo amount.
I just did this today. Here is what I did.
I always let my balances report - I don't care if it affects score yada yada yada - it's what I do and it hasn't affected me yet.
The first balance I paid on the due date. The second balance I got I paid today, (scheduled payments last night, even though it isn't due until next month. Today, I requested the 3x and got pretty close to the full 3x.
I just moved about half of my charge card spend onto the BCE (mostly groceries and a few other things) and that's all.
I think people get a little too nervous with AMEX - I really don't think there is any reason to tip-toe around them. Treat them well and they should treat you well.