For recovering non-combat approaches in-between missions, some sort of downtime mechanic fits in well. For recovering approaches during a mission, I would look into how Burning Wheel games like mouseguard handle generating "checks" by breaking ties in the opponents favor, or getting yourself into trouble, with the addition of "Talents" it makes a pretty easy hack jab from BW's checks and traits.
This game seems great, but I'm just not convinced by the "Shock Traps" battle effect. It has two problems in my eyes. 1) It would be incredibly unfun for a player to lose their action by stepping on an invisible trap. Taking away a player's agency is naturally going to feel bad, but what makes it worse is that it has minimal counter play. 2) It seems like it would encourage a more conservative and less mobile playstyles as players would be to move around where enemies died (this conflicts with drops).
You could handle resting by having to come with an element of risk. This would introduce tension and dynamism to resting & make the question of when to rest an interesting & deep decision. For instance when players rest they need to roll a d6, on a 1 the GM introduces a new complication or threat (like the fortress begins to collapse). Or instead of a die roll, there could be a tension clock players mark when they rest.
