Fallout – Does the cost of reviving a dweller ever change? If so, how much

The quality of items you find is directly tied to the length of time the dweller is out in the wasteland. Their survivability of course is related to their level (health) and the number of stims/radaways you give them.

Basically just wait longer. The longer they are out there, the better chance of getting a better drop. There are no guarantees of course, but if they can survive out there for several more days, leave them for as long as you can and you should get better drops. Since they take no damage or radiation while on their way back, you can wait until they are literally 1 hp away from death before recalling them to get maximum exploration time.

Try to avoid upgrading rooms. Incidents are much worse in fully upgraded rooms than a room with hasn't been upgraded. In particular training rooms don't benefit much from upgrades so I don't bother to upgrade those rooms. I also don't upgrade medical and science rooms, so I can rush them over and over as necessary to generate stimpacks/radaways or to get rushing or incident related objectives. Most of the time I leave these later rooms occupied by a single dweller, and that's enough to deal with any incidents.

The only rooms I do upgrade are the energy/water/food resource production rooms. For example I have fully upgraded a Nuka-Cola bottling plant next to the vault door, and the dwellers there are armed to the teeth. I also make sure that any production room that I have upgraded is fully staffed. I don't bother to try to respond to incidents by moving people around. It never works well. (Though early in the game I did move weapons around. One missile launcher can make a big difference.)

You should also consider your vault layout. Storage and residential rooms should be left unoccupied and placed so incidents in them can't spread to other rooms, or at the very least only to one fully occupied room.

I've also limited the population of my vault to about 110, as there doesn't seem to be much point in going beyond that. It's already pain to deal that many dwellers. I'm not sure if vault population factors into the severity of incidents, but that might be something to consider. I don't seem to have as much of a problem with incidents as you do even in my fully upgraded rooms, but that could be because my dwellers have better weapons than yours. I'm currently tossing away anything that doesn't do least 10 damage on average. At the very least reducing the population of your vault would let increase the damage of the weapons the remaining dwellers are equipped with.

Finally, I'd recommend just putting your phone in your pocket when you can't pay close enough attention to respond to incidents. Unless you're actively grinding certain objectives, you might as well just leave the game alone. You can't have any incidents while you're not playing the game.