An update of my thoughts after some more experience with playing.
I've played on further in my Continent and managed to get all the wind shelters I needed to get all the lieutenants down and expose the overlord. I sucked it up and dumped my shards into wind shelters to do this and focused my entire effort on diving into caves for secret missions exclusively. Since cave diving involves a lot of boss killing, this seems like a good way to farm shards as well. I still think that stashes need to have larger shard piles. Killing a bat will give me like 30-40, but a pile in a stash will sometimes have 4. If stashes held more like 100-200 shards (at least) I'd be much more excited about seeking them out.
I still feel like the map-missions are worthless, and I'd like to have more incentive to do them, because I find the missions themselves to be fun to do. I've never needed a spell drop they provide after the first couple I did, and the only reason I even do them now is because they are in the way when I want to place a structure in that square.
The more I think about it, the more I think that it is a mistake to try and make such a sharp distinction between the three reward-giving tasks (map missions, stash looting, secret missions). I think they'd all be much more interesting if the results pulled in a variety of random rewards (everything that can be provided by a stash or a secret mission), but you didn't know the results until you finished it. Secret missions should return the highest number of things and therefore have a much higher chance of providing guardian power stuff. It would be fine to leave the survivor rescue mission as they are though since the reward for them is meant to be very specific.
If the "loot chests" of all three had a minimum number of shards as a reward (in addition to whatever else they provide), then no result would be completely worthless, since they can build toward buying what you need if the RNG is never in your favor.
Ideally, an "expedition" for me would involve:
1) Find a map mission that sounds interesting.
2) Do the mission.
3) Loot a few buildings in the area.
4) Maybe find and do 1-2 secret missions as well.
I wonder if the game would be improved by providing some incentive to 'stay' in a map area for a longer period of time. That could help counter the strategy of grinding map missions exclusively. The world feels too passive and nonthreatening at the moment, and I wish there was more of a reward for going on 'efficient' expeditions. Perhaps simply a small 'cost' for every map square you traverse, to represent the time spent traveling.