Update from almost 2 years on!
Short Version:
It worked, and we avoided around thousands in taxes.
Long Version:
It wasn't completely smooth sailing. There were yet two more problems and the dust only finally settled last month. Those issues were:
1. Transferring the Shares
As discussed at length either in this thread, my broker (Fidelity) won't transfer shares from a US resident (i.e. me) to a non-resident alien (i.e. my brother) directly. They recommended setting up a 3 step process: Set up a joint account with my brother, transfer the shares to the joint account, and from there into my bother's account.
Only Fidelity don't support joint accounts with non-residents. Nor do any of the other brokers we contacted over the next month with the exception of Interactive Brokers. They don't seem to care much as long as the initial application has a US residents SSN associated with it.
So we set that up and I transfer the shares to the joint account. I have to visit a Fidelity branch in person with ID and jump through some in-person hoops to do this, but there's no pushback or problems. We try to transfer the shares to my brother Interactive Brokers UK account only to have the UI block us. We contact support, who don't have a clue, but we keep at them until we finally get an answer: They don't allow share transfers from accounts where ALL the names on the accounts aren't on the destination account. So you can never transfer from joint accounts to individual accounts.
So we have another chat with my tax advisor, have my brother hit the sell button, and move the proceeds into his UK account. Interactive Brokers have no issue with that. For the paper trail and the suspicion my brother would be slow to reinvest the money, I'd have preferred him to have the shares rather than the cash, but that was no longer an option.
(It then took something like 4 months to close the empty joint account, because for some reason Interactive Brokers thought there was something still in there. As you've probably gathered, I've not been impressed by Interactive Brokers).
2. IRS Initially wanted 50% of the tax avoided
While the notes field in my 2022 tax return (filed April 2023) explained why the sales should not be a taxable event for me, I got a letter from the IRS in the middle of June 2024 titled 'Your tax return does not match the information we have on record'. It says I need to either pay 50% of the capital gain from the sale or supply a signed statement explaining items not agreed with' along with supporting documentation. Both my tax advisor and I think this is just an automated response and no human has looked at the comments put on my tax return. I don't want to pay the tax advisor even more money, so I decide to at least handle the initial appeal myself as it appeared straightforward.
So I send the IRS the signed statement (short and sweet, as per my tax advisor's recommendation), include copies of the 2022 gift form, the signed statement my brother and I filled out at the time transfer share transferring withing the shared account to him (something the tax advisor told us to do at the time), and a copy of the e-mail from the tax advisor saying we had a clear history of correspondence with his firm showing all this was a genuine attempt to gift shares. I was able to file all this with the IRS electronically through their portal, which is better than the 5-6 weeks the postmarks on their letters were showing it was taking for the IRS letters to reach me.
6 weeks later, I get a letter from the IRS saying they need 90 more days to respond, but it's actually only a month later I get the all clear. They've accepted my position and no tax is owed.