A great question which points up a very fundamental issue -how do you organize all this stuff so that you access the right gear quickly??
1. As you said, use for recreation as practice. I know it not the correct term, but repeated use will build that so called "muscle memory" and when you need a particular piece of gear you'll reach for it instinctively.
2. Keep things consistent, control changing/moving/replacing gear.
3. Keep things modular so you can swap out modules, but modules should follow the above. A winter and summer clothing module should have similar items in a similar place inside.
4. Make a habit to put stuff back when you use it so its there next time.
5. You begin to move from just buying some gear to having a prepared lifestyle. I have a dairy/journal just dedicated to gear changes where I can write my thoughts and reasoning as to why I moved/replaced/changed something.
5. Some pre-made checklist/plan to follow too so you can go into autopilot in the situation. One might take a look at military manuals and think its a lot of redundant paperwork but in the situation your stressed and might not think/remember things clearly so you have those checklists/papers/manuals to fall back on.
You almost always have a few minutes to gather your stuff, even in an extreme bug out. We had to leave our home a few years ago in the face of an impending wildfire, and it was good to have a basic pack assembled, but there was still time to throw in some potential essentials, like my good helmet..
I use our 'neighbors up the hollar ' as an extreme bug out example. They were about a mile or so up the dirt road from us and had bought the small farm after its previous owners passed. Old farm house with a wood stove in the living room somehow caught fire one winter night. Stove was along the wall between the living room with the front door and kitchen with the back door and then a hall to the bedrooms. Fire blocking exit from the hall to either door so the family had to go our bedroom windows. Car keys, shoes and coats hanging by the front door as a lot of people do. So the oldest son ran down the snow covered road the mile to our house, barefoot and wearing only pajamas, to use the phone to call the fire department.
So they had to bug out really quick and with no preps and no time to grab anything ( zero minutes,worst case scenario ). I tell everyone, keep your keys and phone next to you when you sleep so you have them if you go out the door.
So even though I've never done SAR I keep my pack ready to go. I have an old antique chair my grandmother gave me sitting beside my nightstand. My pack stays there, phone and keys on the nightstand as well. Its my recreational pack also, hiking, biking, fishing, whatever. And like yours can go down to just a water bladder and minimal other gear. It has one of those FroggTogg thin flat foldable rain jackets and pants, spare socks and my shoes I use for hiking and biking, and spare keys so if I would need to go out a window I have enough to not have to run down the road barefoot.
Part of keeping organized and knowing where your gear is requires not changing it too often. Change one thing at a time and don't buy anything unless you know how its going to fit in your system. That has a secondary benefit of keeping spending budget in control too.