I was especially intrigued by the idea of, in effect, doing price discovery on my legal values:

Yes. I think that's very elegant.

Maybe I'll try to make a separate post on them.

Do it!

The practical burden of all this research into the various "laws" available

People in the market for law would be demanding both:

• To be subject to laws that they prefer, as often as possible
• To be subject to a predictable (harmonized/standardised) system of law

These two desires can't both be perfectly realised, so there'll be some sweet spot between the two. The market is the best mechanism for discovering where that spot it.

Back when I was a libertarian I tried to imagine private alternatives to the FDA, and it ended up so convoluted I had to think in the end it was something of a natural monopoly.

Private alternatives (in the sense of firms that strive to provide credible assurances of safety) already exist. I made a video on that too:

Letting laws be determined by market forces basically means the rich get to set the laws

Sort of. But more accurately: It allows the rich to try to buy the laws they want from the other people who will be subject to them too. Ie. The rich might get the laws they prefer, but if they do, they'll be compensating those who'd prefer other laws on an ongoing basis, by effectively subsidising the legal costs of those others.

if I am rich enough to contract only with REAs that will ruthlessly pursue the interests of their very rich clientele

I don't think such agencies could exist under this order. The profitability of the agencies is tied to their ability to avoid conflict, which means they have to reach peaceful agreements with their competitors. A 'RICH-DEFENSE-SCREW-YOU' agency, and the arbitrators it used, would be cut off from the rest of society if they failed to make such agreements. They'd be outlaws, and would (imo) lose.

Bear in mind also: the most profitable firms currently are not usually the ones catering to hyper wealthy clients only.

So 'rich makes right' doesn't reflect the situation correctly.

Why wouldn't they simply take from the otherwise defenseless rich? Because violence is "expensive"?

It is. The violence they should be thinking about is the prospect of violence they'd face from a coalition of all other defence agencies sensing an imminent threat to their clients (and to their own ongoing existence). Hence the 'war against the rest of society' meme. Not a smart business move.

Would that REA be shunned by others? Sure, but if they're powerful enough, it doesn't matter, and if they're not powerful enough, then the same problem repeats with that more powerful REA

If an arbitrarily powerful malevolent entity is posited, any socio political system will fail, obviously. The relevant question is: "Does this system do better or worse than the alternatives i'm considering, with regard to factors disincentivise that kind of abuse" I think it does much better than systems that centralise political power, as the status quo does.