I voted Navigator, and it looks like I'm the only one. I'm not too surprised, but I thought there might be at least a couple. When I put this poll up, I was fairly sure it was the right answer, but looking at sims it's really close, but without adapting Duchy buy rules, Sea Hag is a slight (2%) favorite. I think the 3 reasonable choices are Hag, Horse Traders and Navigator.
I think the most distinguishing aspects of this kingdom are:
1. Curses
2. No trashing
3. No drawing
4. No non-terminals
5. Not even any terminals that are good past the early game!
There's basically nothing you can do other than grab a few terminals (preferably Mountebanks) and money.
Nomad Camp doesn't have a good enough chance of getting you that early Mountebank to offset the fact that it immediately turns into a Woodcutter after that. Navigator can't get you a Mountebank play on turn 3, but it can get one on turn 4 at least half as often and is much more useful later.
Moneylender's trashing is really not that useful, since Copper is not that bad, and you're more interested in cycling early to play cursers than to have the added later cycling from removed Copper, which makes Navigator better here too.
The bots I tested are the Mountebank bot with a rule to buy one Nav or HT at the start and the Sea Hag bot changed to buy one Hag and one MB instead of 2 Hags.
The results I got (2-player, 4/3 start) are:
Hag 49 > 47 Nav (58-37 and 40-56 depending on turn order)
Nav 50 > 46 HT (58-37 and 40-55)
Hag 50 > 46 HT (58-37 and 42-54)
All other openings added to the Mountebank bot lose handily to these.
HT and Nav stand to benefit more from smart play, since you may want to keep a Curse in hand to hit a money threshold with HT, and I'm not sure how smartly the sim handles choosing when to discard with Nav. The few samples I've seen haven't done anything stupid like discarding a MB early, but it surely doesn't consider at what times $5 is a good hand in the late game. Either way, these are all within the margin of error of dealing with endgame VP buys.
My rationale for thinking Navigator would be best is that it allows for the most plays of your Mountebanks and eventually your Golds, which is basically what the game should come down to, but the other two options do have their appeal as well.
If there were any other decent $5 in the kingdom, like Lab, Cartographer, or Vault, I think the best opening would likely be Sea Hag, since you don't want to be spending your $5 hands on Mountebanks when you can get a Curser on a $4 hand. But without an other options at $5, you should be happy to buy Mountebanks. As the kingdom is, Sea Hag still might be best, but it's at least really close.
So, unfortunately, I think like Rabid did in the first edition of this series, I failed to give you a board where you don't want to open Sea Hag (which has to be pretty rare without good trashing or Lighthouse).
The actual kingdom was in a 3-player IRL game, with MB, Hag, Nav, and HT, plus a bunch of junk, which I replaced since (1) I don't remember what it was, and (2) I wanted to see if people would pick things like Nomad Camp, Moneylender, and Feast. The interesting thing is that if you put these 3 bots against each other in a 3-player sim, the Sea Hag has no chance, losing something like 37-37-20, but if multiple players go Hag, it's very close again. This of course is a general trend in 3-player, where the players who play similarly will be favored against the odd man out. But even if you're the one not going Sea Hag, you're still in good shape with Nav, and probably favored with HT (since reactions are better in 3-player).
