Under "getting green" and "discard for benefit" I feel like you didn't mention the best synergies here: Warehouse/Dungeon. This seems way better than Storeroom, though still probably not actually viable.
You also don't mention Scout/Crossroads (jomini mentioned this too), which I feel like at least deserves a nod here. My opinion is that Scout/Crossroads is only useful in puzzles where you can assume you get perfect shuffle luck. The problem is that Scout is just as likely to hurt a Crossroads for your next hand as it is to help a Crossroads in your current hand.
Also there is problem that you would draw more from another crossroads, assuming that there is some support as pure scout-crossroads is worse than bm.
No. Xroads 1 draws you 3 (number of cards you search) * % green in deck. Xroads 2 draws you (3 + xroads 1) * % green.
For instance. if my deck is 33% green. Xroads 1 will draw me 1 card and Xroads 2 will draw me 1.33 cards for a total of + 2.33 cards at the price of two actions (the +3 being flat and non-scaling).
Scout/Xroads draws 4 * %green from the Scout's draw power and 7 * %green from the Xroads that is played next. Basically any card in the Scout search space draws twice.
With 33% green this works out to be 4/3 cards drawn by the Scout and then 7/3 being drawn by the crossroads for a total of 11/3 or 3.66 cards. This also takes one fewer action and lets you sort the top deck on hands with limited draw (so you can draw some more).
In general, if x is the percent green the two xroads in hand will draw 3x +(3+3x)x or 6x + 3x^2 while Scout/xroads will draw 11x. Scout/Xroads then draws more IFF:
11x >= 6x+3x^2
11 >= 6 + 3x
5/3 >= x
as 1 >= x >= 0 there should be no deck composition where Scout/Xroads hands are expected to draw less than Xroads x2.
Adam: Goons engines just churn points compared to much of anything else. With trashing, I can churn 9 VP per turn and
attack you every turn. Piling down 8 provinces instead of 4 takes a lot longer with Smithy-BM variants Prince of Scouts is one of the slowest Goons engines, but Goons engines are just that good. BM is, much, much worse when it cannot start faltering and slowly drags it way across the 41 VP line.
Using Tr with the Scout/Xroads is to allow you greater flexibility. Ideally you want more Xroads than Scouts, but you run into problems that having hands with just Xroads lowers your draw potential. Tr gives you the choice if you track your deck of loading up on green first (Tr -> Scout), or drawing for more (Tr -> Xroads); Tr is also phenomenal at getting you value out of the green you draw (e.g. Tr/Baron/Xroads is almost good enough to play on its own, using Scout would make it a pretty decent-ish engine).
Pool prefers Scout when draw is still an issue, because Scout can let you use the discard (top deck a copper) and ensure more than cantrip draw if you see just two actions in 4 cards. Candlestick maker does a different function - coin and +buy, a much better comparison is with Vagrant or Pearl Diver. With Vagrant you can snap up greens and it is cantrip so it normally beats out Scout here. Pearl Diver, on the other hand, is only good when you have a low green amount. If you are trashing down with Counterfeit, Scout doesn't take too long before he draws an average of at least 1 card and 4 card top deck reordering is better than two card deck reordering.
Pile control sounds good, but if your opponent notices they can just snag VP a bit sooner and then you are carrying around a lot of space inefficient cars. Again, it isn't that Scout is often good, but that at times it is better than other stuff. Ramping up to the third pile needs at least two turns; during that time Scout has a small chance of swinging a single province (or colony) turn into a double.
