For the last 4 years, have you filed an AMT return (form 6251) with accompanying AMT1116's?
My understanding, and I could be wrong, is normal 1116FTC's are a different animal to 1116AMTFTC's. To use the carryover for AMT, you need excess AMTFTC's. I believe, in general, calculations are the same (allowable available tax credits minus the "Limitation" amount equals excess credits for the tax year). AMT 1116's are calculated differently than normal 1116's (see instructions on 1116), although the form is the same.
When I've used carryover before, I've enclosed the "carryover calculations sheet" with the return. It's asked for in the instructions, but I don't know if a professional would include it. My guess is "yes".
Hopefully, someone with the knowledge will comment concerning FTC's for normal 1116's versus AMT1116's.