Thanks, all.
I thought 1040NR was for non-residents (aka no longer living in the States). So all I have to do is the 1116 form (with the usual 1040), and not the 8833 form (which references the 1040NR form). I am going to try TurboTax and see how that works, when it's time (aka the 2018 tax year IRS filing). At present, because I don't know what my taxes will be for HMRC 2017/18 (officially), I can't pay them, so I can't get any sort of IRS credit for IRS year 2017. It'll just be a carryforward situation permanently, I guess, as my UK taxes will be more than my USA taxes.
So I can go ahead and stop withholding on my pension so that I have the cash to pay HMRC, and then take the credit for what I pay HMRC off my taxes next year.
Appreciate all the help. REALLY appreciate the help. (The IRS scares the willies out of me.)