I've just added Enhance (ONLY IN SHELTER GAMES), which I think always works?
Yes, you're guaranteed to have a hand with at least $3 and a non-Victory shelter if you open 3/4.
The following Events/Projects also work:
Scouting Party: Open Double Silver, buy SP on T3 unless you have $5+ or three Estates/Shelters in hand (in which cases you don't need it to get $5 on T3/4).
Banish: Open Silver/Exile (in any order) and exile the Estate/Shelter from your $4 hand.
City Gate: Open Silver (or double Silver) and buy CG on T3 unless you have $5+ or three Estates/Shelters in hand (in which cases you don't need it to get $5 on T3/4).
I think the list of Events and Projects is now complete with these additions, as I've considered each of them that can be bought with at most $4 or with debt and wasn't yet listed. (I'm not quite certain in the case of Pursue, but I think you can't make it work in all cases, no matter whether you try to Pursue silvers on T1, T2 or T3.)