How do you deal with this practically? If an American moved to the UK now (after April 6th of this year), how would you recommend dealing with it? Even if your answer is to get a tax accountant, do you recommend doing that early?

Not an accountant, simply talking from my experience.

If you're moving after April 6th you're probably going to be fine on the UK side. If you have any US income in the tax year you can claim either split year (on the foreign pages) or treaty residence (using hs302) in the US up until you move (assuming you file Self Assessment, most PAYE employees don't, though you strictly should given the foreign stuff). HMRC is way nicer and easier to work with than the IRS. It's a breath of fresh air. This is pretty simple, but UK accountants are also pretty cheap.

The trouble is on the US side. If you're an American citizen you are liable to pay US taxes on all your income. If you're outside the US for most of the tax year, you can claim the FEIE and if you make less than ~$130,000, you have little else to do. If you're PAYE in the UK, you can claim the FTC on the cash basis in the US and you will probably also be fine. This is all fairly simple to do, and depending on your comfort levels you can probably do it in TaxAct or myExpatTaxes online. You also need to file FBARs and possibly 8938s every April. The trouble is if you are a sole trader or similar in the UK. This makes the FTC really hard. You will probably want a US accountant with knowledge of foreign tax if you are self-employed. Buzzacott is a firm I have seen do some good work for friends of mine with complex US and UK tax filings (though I have not personally used them). You can expect to pay thousands of dollars in tax prep fees every year if you use an accountant. This stuff seriously exceeds the knowledge of most US CPAs, so you will need someone who specifically advertises this.

Also as an American you need to avoid pretty much all of the useful tax-planning tools here in the UK. You can't really have a S&S ISA, or any other kind of tax-advantaged account other than a workplace pension without it all going totally bananas on the US side. You also can't own a UK limited company (more than ~10%) without getting whacked with crazy 5471 reporting. Same applies to UK trusts, you can't touch them without 3520 reporting (even for trivial things like life insurance trusts here in the UK, and even certain pension products). Many banks and financial services providers won't touch Americans with a 10 foot pole.

On the other hand you can potentially save a lot in taxes if you ever move back to the US if you've accumulated a lot of FTC carry forward. You can also probably pay a pretty minimal amount of US student loans if you're on IBR because the payments are based on your AGI which will be artificially low.

The US needs to abolish citizenship based taxation and chill out on the reporting requirements (which are generally the worst part) for people who generally live abroad. However, I wouldn't hold my breath. Even though the current admin has said they'll get rid of it, I just don't see that there's much political capital to spend on this issue. There aren't that many Americans living abroad, and most Americans don't give a shit about this sort of thing.

I already live in the EU so know about a lot of the irritations of being an American abroad, but I was surprised to hear about the whole shifted UK tax year. I am considering a move there so I'll just remember your post and use it as a starting point in dealing with it all. Thanks so much for all the info!