Ok, so not hypothetical.
I have two income streams. A US pension and US social security.
I am a US citizen living in the UK. I'm not a dual US/UK citizen.
My US social security is taxable only in the UK, not in the USA.
So that leaves me only the pension taxable in the USA.
IF the HMRC decides that the pension is taxable in the UK, between the UK tax on it and the tax on the SS I'll have enough HMRC tax credit to wipe out the US tax. With plenty of credit left over to spare.
So, there is only one income stream to apportion when using 1116 FTC. The pension, if it's taxed by HMRC.
If I know what I'm going to owe HMRC for April of 2018 tax year end, I can pay it before Dec 31 2018 and count it as a foreign tax credit against the IRS tax for the IRS 2018 tax year. I can carry back any leftover credit to cover IRS tax on that income for the 2017 IRS tax year. So at that point "paid" v "accrued" is kind of a moot point.
If I ~don't~ know what I'm going to owe HMRC (if anything) for the end of 2017/18 tax year until after 31 Dec 2018, I assume I can plop down enough cash into my HMRC tax account to cover the worst case scenario prior to 31 Dec 2018 so that I can claim it as credit against IRS taxes. And carry back any leftover to IRS 2017 tax on the same type of income (pension) via 1040X. That would require use of "paid" on the 1116 form(s). And be kinda messy.
It would seem that the only use to me for "accrual" on a 1116 Foreign Tax Credit form would be if I couldn't get all of the 2017/18 HMRC worst-case tax paid prior to 31 Dec 2018. OR if HMRC said I only owed X for 2017/18 and then later came back, after 31 Dec 2018, and said I actually owe 2X. At that point I couldn't count the 2X against my 2018 IRS taxes if I had already taken X using "paid" foreign tax credit for 2018. Because I would not have actually paid the 2X, only the X, in 2018. So I'd just be out of pocket that cash. If I had chosen "accrued" and HMRC popped back up in a year or two and said, no, we now think you owed 2X for that year, I could go back and file a 1040X to replace the original 1116 stating X with a new 1116 stating 2X, no?