I know nothing about TuroTax, other than it's not designed to handle international returns. Nonetheless it will work most of the time, but not all the time. This maybe one of those times. Nowhere is there any guarantee that a US person abroad will never owe the IRS, even with foreign tax paid offsetting US tax. It can occur. In the past I've had to pay AMT tax, but the rules that caused it to occur have changed.
I don't understand " .....Foreign Earned Income and Exclusion section and then the UK taxes I've paid Foreign Taxes section of the Deductions & Credits page". It may be time to ditch the FEIE (2555) and start using FTC (1116). Since you're using TurboTax, it should be easier than figuring it yourself. There is a provision in AMT to allow for foreign tax credits which pertain to AMT.
Specify FTC form 1116 for all foreign income and see what happens.