How am I supposed to combat the increased difficulty of incidents late-game in Fallout Shelter?

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.

There are two* things you can do to reduce the severity of incidents.

First, know that incidents are based on the level of your Dwellers. If everyone is level 50, you'll have much harder incidents than if you've got a bunch of level 1s. You may notice that incidents seem to get easier after a rash of pregnancies ... this is why.

Second, you can build in a checkerboard pattern. Disasters won't spread diagonally so you can just evacuate a room and it'll go away after 15 seconds.

*There a few other things which I'll edit in later but above are the big ones.

Im playing survial mode on the steam version, got 55x lvl 25 dwellers with 7+ damage guns and 8+ strength/perception/agility and all lvl 1 rooms

• long story short : do not upgrade any rooms without being totally aware of the increased risks because it will end you

Death claw raids aside i had my vault under total control, so i upgraded my power,water,food rooms to lvl 2 and literally they could not kill a radscorpion before it would spread to the next room, even in my first power room that had the highest strengh and even some 13+ damage weapons

Ive had my science and medbay rooms at lvl 3 for ages but if i fail a rush on them i would remove the 1 guy i had in there and if its a radscorpion i would usually just wait until it spread to one of my defended rooms but with a 16% and 26% chance of failure this rarely happens and i find i never need to rush out stimpacks more than once or twice since im always floating at 55 capacity

the trick there is that the radscorpion will scale to the room it spreads too so even though its a L3 room that spawned it i can kill it with all my other lvl 1 defended rooms, and ofcouse have your high risk rooms seperate from other rooms so all other incidents aside from radscorpions are easily dodged

the best advise i can give is that you should fail a rush in a defended lvl 1 room to "reset" the incident timer, and if you opened the vault door be sure to trigger another incident asap otherwise the game will probably hit you with death claws instead sometime soon, oh and play on the pc so you easily backup/restore your save with a couple of clicks on your desktop since theres been dozens of times i log and someone dies or deathclaws appear or a radscorion goes on a rampage right as im in the middle of trying to sort my training rooms or send out a quest and everything just goes to hell real fast