I'm open to the possibility that I'm dead wrong and my hatred for Mandarin openings just shows how little I understand about this game, but opening Mandarin/Mandarin/Mandarin/Upgrade and then upgrading a Mandarin into a Gold (best case scenario) on turn 5 isn't a "quick gold". In my mind, in nearly all these scenarios you're losing a turn to put a card in your deck you don't want.
1. Upgrade/nothing seems a lot better to me the times your opening buys don't immediately collide, which is pretty often.
2. I guess there's something brilliant in putting terrible cards back on the deck so you can draw them again. I'd suggest Library/Hamlet is better so you can keep playing (hopefully good) action cards after the Library, though. And, not draw that Estate twice and stuff.
3. If there's no better $5 cards around, I guess this could beat BM on some boards? Or better $4 cards. Or just Silver maybe. Again there's something brilliant in going through lots of trouble setting up sweet Menagerie draws so you can draw those Estates again.
4. Governor/nothing seems good here. Forge is probably a joke on a Governor board, KC is probably too slow a fair amount of the time unless (again) your openers happen to collide immediately, and if they don't, you've wasted a turn and have a bad card in your deck.
I mean, like with nearly everything, I'm sure there's corner cases where these cards come up, and no other card in the kingdom makes anything else viable, and it might actually be good. But it seems to me that this would be pretty rare. Or, I'm just dead wrong about Mandarin of course. Anyway, rereading this it might come off as harsh, I didn't mean it like that and I hope you don't take it like that.
I don't think upgrade/nothing works out as well as Mandarin/Upgrade/nothing. Here's why.
Upgrade/null has a 4% chance of getting a second upgrade on T3 and less than an 8% chance of picking it up on T4. The only way to get a second upgrade is to draw exactly 5 coppers. Otherwise, you out of luck and buying silver unless you have another good card at 3 or 4. Until T5, there is a 0% chance of getting a goons.
Mandarin/Upgrade/Null has many ways to get high power cards on T4:
1. It can also hit 5 coppers - which unlike Upgrade/null means next turn you likely will be able to get something good (maybe even a third upgrade).
2. It can hit 2c/mandarin/whatever - a very statistically likely hand that gets you an upgrade.
3. It can hit mandarin/upgrade and get a killer early goons.
4. It can hit 3c/Mandarin/whatever and get a goons
I could be wrong on this, but I think Mandarin/Upgrade would lose tempo early to upgrade/nothing, but gain it back later through the purchase of additional upgrades or by upgrading the mandarin to a killer six coin card (i.e. goons).
For Mandarin/Library vs hamlet/library, yes you draw a "crappy" card again, but you have gotten 3 coin for the privilege. Hamlet/Library needs some a strong source of cash and playing Mandarin eats an action, lets you draw one additional card (to replace the mandarin), and takes an action. So if you have the actions, then Mandarin's next effect in library/hamlet engine is -1 action, +3 coins, +1 card. That is not bad. It is no worse than any other terminal silver you'd spam in a library/hamlet engine to keep the draw coming and argueably better if there is any trashing (e.g. forge or spice merchant) as you can double dip on cards to put back (e.g. play hamlet, mandarin, library, hamlet, mandarin and place the same estate back twice). Forge in particular would tempt me mandarin/lib/hamlet as I can quickly forge to a gold and toss all but a few coppers in one go.
3. So you draw the estate (more likely copper) again? Who cares? You now have +3 coin and +2 more cards. Yeah it isn't as good as festival, but playing you'd move through your deck more quickly, and get up to 8 without buying golds (though I'd likely get one).
4. Governor/KC is blindingly amazing. It's almost as good as hitting a TM (yeah I know the other players get silvers, the golds go into your discard, etc. - it still is almost that good). As an added bonus late game, anyone looking to remodel their gold into a province has to worry that you will remodel a KC into a province as well. KC/Mandarin is an assured province or plat; and you can get cards out of your hand and still play it. My only real question is, will governor/nothing be faster than the Mandarin. Like with upgrade you lose a turn, like with upgrade you have many more options on T4 to hit KC. Forge and governor work quite well togethor; the only real trouble is the opportunity cost of forge. Your opponents will likely increase your size, send you silver etc. and you can then forge silver + governor into a province or silver + estate into more governors.