My wife is self-employed, on a small scale, so can try to help. But key question up front - you talk about leaving money in the business, is there a separate business entity? My wife is a sole trader - effectively, she is the business and the business is her, there's not really any separation in the finances. If you've got a limited company (sounds like not a partnership), the rules are significantly different, I can't help there, although I know the IRS throws some complications about ownership of "foreign" corporations.
For a sole trader:
HMRC reporting is straightforward enough. Need to calculate revenue, take off expenses, the rest is taxable income. Self Assessment also calculates NI on that income.
IRS reporting is very similar. I don't know for sure how the FEIE interacts with self employment (we use the FTC, which works well here). You will need to consider self employment tax - you can choose to inform the IRS that you are paying UK NI and thus don't also need to pay US social security/medicare. That's a slightly separate process, involves getting a certificate from HMRC. Or you can choose to pay US self-employment tax and you'll build up Social Security contributions as well, some people choose to do this.
The dates are a big pain - effectively, we do a year-end close twice a year. Once for the US 01Jan-31Dec tax year, and once for the UK 06Apr-05Apr tax year. Both countries want you to include the income in the year you actually get it. You can defer filing US taxes until after the UK year is over, so you can do all the calculations at the same time (i.e. on 07Apr you calculate income and expenses for both tax years, but the numbers you report to each country will be different). Easy to file a US extension so you aren't rushing to do this between 06Apr and 15Apr - just extend US taxes to October. If you were using the FTC, you'd want to make sure you file and pay UK taxes before 31Dec; not sure if there's any catch there for FEIE.
Both countries want estimated tax payments, if you're making/paying enough tax. Haven't had to deal with that yet, but certainly worth looking into.
The bottom line good news is that, despite the pain in lining stuff up, you don't have to pay double tax - in most cases, your US tax liability will be zero. The main opportunity for double tax is with NI + US self-employment tax, but you can get out of that.