When paying AMT, might it make sense to take standard deduction even if it's more expensive?

Due to an ISO exercise, I must pay AMT this year. But this was a one-time thing: I will probably not need to pay AMT next year.

Since ISO exercises are considered a "deferral item", my understanding is this will result in being able to claim an AMT tax credit in subsequent years.

If this is correct so far, is the credit limited to the difference between what I would have paid without AMT, versus what I had to pay? In other words, the extra tax I must pay due to AMT: will I get it back eventually?

I’m wondering because AMT does not allow the standard deduction, and my itemized deductions don’t sum to anywhere near the standard deduction. So:

• If I itemize: I pay less tax this year, but the standard tax liability is higher, so the difference between standard tax and AMT is less. (And maybe this limits the credits I can later claim?)
• If I take the standard deduction: I pay more tax this year, but standard tax is lower and so the difference between that and AMT is more. (But maybe this means more credits in later years?)

If AMT credits are limited to the difference between standard tax and AMT, might it make sense to take the standard deduction this year since after the credit is claimed in subsequent years I will have paid less tax overall, even if I paid more this year?