I am trying to figure out how to intentionally trigger a “deemed distribution” of my 401(k) but there doesn’t seem to be any obvious process for this.
I’m not clear on what you’re trying to achieve with a “deemed distribution”. Most people would want to avoid that — it leaves you having to pay tax now on money you’ve yet to receive, and may in fact never receive. Almost always undesirable. (FWIW, the way to trigger a ‘deemed distribution’ as you ask would have been to have rolled the 401k into an IRA before renouncing. The rules for 401ks and IRAs are completely different.)
Maybe I’m missing something, but can’t you simply take a withdrawal of the entire 401k balance? This would be an early withdrawal, so US federal income tax plus a 10% early withdrawal penalty. If done after leaving the US though, you escape any state tax on it, which could help offset the 10% penalty.
Assuming that you have no other exposure to the US’s soviet-style exit tax — that is, unrealised capital gains below $700k or so, no likelihood of gifts/bequests back to US persons (see section 2801 for that), and no other US based retirement accounts — a full 401k withdrawal may not be a bad option. Once done, you’re out of the US system entirely, never have to think about it again, and can move about the planet and invest freely.
All this assuming you desire a ‘clean’ exit from US tax. Other less clean options are of course possible.