I ran a handful of tests pre-Shelter reveal. Each was a solitaire mini-game of small kingdoms and to a 12 turn limit in order to get a microcosm view of some strategies. Part of the algorithm was greening duchies in turns 11 and 12 (when falling short of Province).
I tried five games of a Rats/Hermit opener, with the intent to pick up Conspirators and Sages, the latter largely via Hermit. The first game was ultra smooth, Hermit keeping the Rat population to 1. The trash pile was full of Rats, Coppers, and Estates. It achieved 3 Provinces and looked like it would keep grabbing one a turn.
The following results were mixed. Inside the small sampling, there were two 2 Copper turn 3s. All in all, it was not so great, but the inclusion of Sage was probably a mistake. I did it to add more DA flavour, but it's really cost for cost as good a sifter as Hunting Party or Golem, so trashing was made pretty irrelevant. The initiative to run a Rats/Hermit test was really the notion that your deck size would seldom increase; each two turns you'd have only 1 card left in your deck. (Of course, Sage makes shuffle control difficult, so another test might be in order with a different strategy).
For a control, I played a game starting Sage/Conspirator with no Rats. It collected 3 Provinces and a Duchy (and had all 3 Estates) though the game might have been anomalous, doing it more with Golds than powered Conspirators. I hit $6 turn 3 and often afterward.
Next was a Conspirator/Hermit combo... no Rats, Hermit to grab Sages. It hit 3 Provinces by the end, and it felt like it'd be consistent.
I tried a couple games with Forge and Laboratory available, starting Rats/Silver. The first game was stagnant, getting $4 in turns 3 and 4, Rats coming up in the 5th turn. I gave it a redo, added a Conspirator to the mix, and it smoked! A turn 6 purchase of Forge powered it to 4 Provinces by the end of turn 12 though not much else in deck besides a couple Rats, a Copper, and a Silver (and enough $ on the 12th turn to buy another Silver.) I think this was darned lucky, but it was interesting to see.
Lastly, I varied it up, going Remodel/Village with Rats to trim Coppers. The goal here was to instead see how many Grand Markets could be gained by turn 12. The first attempt was a disaster, Remodel coming turn 5. I still managed to get 3 GMs. The second was much more efficient, getting 4 GMs.
EDIT: Emboldened openers