If you’re from the EU you can just move to Ireland for five years and then move to the UK after getting Irish citizenship. The housing situation here is bad, but once you get that sorted it’s a very nice place to live.

Statistically Americans are not, in fact, running away from the US.

You need to do a lot more research on visas. You can’t just get a stamp 4 in Ireland; the only people it’s just granted to are spouses of Irish/European nationals. Ireland has no work permit option for self-employed people, period.