I've had great success with the upgrade-heavy small-deck style.
If you scroll down to my long post you'll see a winning run on Adventure with a Scorium Amber as my only purchase, and several other variations powered almost purely by Prospect.
Prospect usage:
Focus your Prospects on 1-2 cards of each resource as much as possible rather than splitting them around.
Do use Prospect to buff both resource types.
Do buff your starting resources; I am typically leaving the opening expedition with one buff on one Ore and on one Scorium.
Early on you want to prioritize using Prospect again on your already-buffed cards over actually playing multiple buffed cards, unless you're going to miss a Scorium goal or you're trying to hit a particular Ore threshold (like 50 for the first Hourglass).
Do consider moves like Prospecting one resource card but playing a different resource.
Do focus buffs on special resources (in your screenshot that Geode should be at 10 and once you get 1 Scorium Pandorite almost all the buffs should be on it).
Shopping:
I very rarely re-roll the shop.
I like the 15-cost Hammer early on my most-buffed Ore but I'm not taking further Hammers unless I have a specific reason or I'm mega-rich.
I take as many as I can get (in roughly this order) of Hourglass, Lens, Ingot (until the last few rounds), Dynamite, Brush & both Geodes (but only once the Geodes I already have are buffed to 10).
If I'm rich or struggling for Score or starting Day 10, I consider Helmet.
I'm also looking for a few build-defining cards like either Amber, Scorium Pandorite, Scorium Meteorite, Smelt or The Creature. I don't necessarily take more than 1 copy of any of these and usually my build will end up with 1-2 total of these cards.
I often end with a deck that is effectively 5-7 cards plus however many cards I can play for free and which replace themselves (like Ingot and Lens).
Mineshaft isn't ideal for this style of build but as an effectively 10/10 mineral that *might* turn into a self-replacer it's worth considering also. It provides good economy early in the run so if you're running out of steam in the middle turns a 1st or 2nd shop Mineshaft might help.
Unless I'm deliberately trying to make some other build work I'm generally not taking any cards except the ones I just listed. Instead, almost all my money is going into Hourglass, Dynamite and cards that replace themselves for free while giving some benefit along the way.
The fewer non-replacers you buy the smaller your effective deck and the more money you have for Hourglass/Dynamite, both of which will mean you get to Prospect more often.
I basically start the game Prospecting every other turn and often by midgame I am able to Prospect every turn. It only takes a few combats of putting out +18 upgrades to get a couple of resource cards very large.
I think you are overlooking axe it doesnt play as nice as compass with amber but playing a resource for free with the draw is huge especially early before you have your deck super slim and i also think you are underestimating kaz (score in particular) it basically solves score in the early rounds letting you focus almost entirely on ore or upgrades and gets stronger as you add cards like geodes that are very cheap and upgrades on them are almost never a waste because you will play them every time you see them similar story on meteorites but not quite as good because they dont replace themselves
Thanks for all the tips. I focused on devising a strategy and managed to get a couple of wins by pushing ore in early game and spending extra on upgrading the scorium. I also had a some succes with Jeroba since it takes up less energy than Prospect, and the creature really seems to help with going through the whole deck each round.