Just my two cents here since this sounded very familiar and sounds very much like what I dealt with. No pain on starting the run, it would settle in exactly 15 to 17 minutes into each run (I dealt with it for years). Never got worse, never any consequence to running through it. Rest did not help. It was not the trochanter itself, but rather felt like something was very very tight over the area and tearing off it! I'll tell you what I did that really helped, but take it with a grain of salt as everyone is different and it goes against what some people may say. This area, your abductors/stabilizers around your hips/glutes need to stabilize and not be loosy goosy so I had to cut out the foam roller just over that area. The foam roller and stretching will inhibit the muscles and you want them FIRING, not taking a break. That is where I go a little against the grain, not a fan of the roller or stretching (if something has the full range of motion, no need to go stretching beyond that). There is a time and a place for it, but not all the time
Make sure you ADDucutors are not overly tight.
It sounds overly simple, but here's what I did:
1. gave the roller a break and stopped stretching it (you don't want a loose IT band anyhow and can't really stretch it)
2. did a dynamic warm up-I don't know why this helps so much, it just does. I did the hold onto a wall or chair and really swing the leg way forward and way back, straight up, straight back for a good 15 to 20 reps at least. Then grab the wall/chair, etc and swing the leg left to right-you may hear a nice free hip adjustment during this. If you need pics or a video I will try to find something. Both legs about 2 sets of 20 swings and really get it going.
3. Simple side steps where you're stepping to the side but have to lift your leg really high and over something. Again, might be hard to visualize.
4. I put a little pad on the side of my arch and it bumps my arch and reminds my foot/adductors to do it's job. Not a correction thing just a "reminder" for some muscles as I run in super lightweight shoes.
If you supinate (on the outside of your foot a lot) those muscles will always be somewhat taxed so it's just controlling it as much as you can.
Oh, and one more thing. If you truly have lazy glutes that are not doing their job, the magic trick is to walk backwards on the treadmill for 10 minutes a day. Don't hang on and drive the feet back and walk forcefully/purposfully, not need to go super fast. Poke that glute and remind it to do it's job while you're walking. Don't be surprised if on the affected side you can barely walk backwards at first and may almost "limp" a little while your body figures out how to do it. Yes, I've had people ask "why are you walking backwards and poking your butt/hip?" but who cares, it works
It's usually the glute medius that gets lazy.