I had the same problem finding info before I went also. I thought because if was so difficult to find info on, there must be something worth keeping quiet about.
For me, I was a student at MK a school when the command master chief from the MSRT came and asked if anyone was interested. Had an interview with him and a PT test to make sure I could meet tier 1 standards (easily found in Google). Got orders.
Reported to "green team" after a school. Green team consists of green members to the unit. Basically the "selection" part. Lots of PT, flat range stuff, just preparing for "AP Hill." Did the swimming part and learned how to ditch kit and all that, went to dunk tank simulating crashed helo, etc. basically 0% attrition, point is judy to prepare you for upcoming schools. Each green team is different, but when I left the green team was completely unlike ours. They were doing a lot of chanting and boot camp style workouts. Lot of "hoo yahs" which was funny.
Then came "AP HILL" which is first stage of training. Takes place at fort ap hill. Forgot how long it is, few weeks I think. O courses, barracks, land nav, flat range, tons of PT, only eat MREs. This stage is tough for sure. I ended up getting a pretty rare sickness from a tick bite (they're everywhere there, multiple bites per day). Fell out at range, spent couple days in ICU because they wouldn't figure out what was wrong. Got to move forward with training because I was almost done anyway and not a slacker.
Next is BTOC. Forgot how long it is. 6 weeks maybe? Ours was run by CACI guys, all retired SF, SEAL, etc, but I think every other class is taught by CG members. Might be different now, Google coast guard BTOC. My team had 8 people from all different DSF units and 4 graduated. Others got kicked for safety violations and all were from other units. Other units don't (didnt) go to AP hill like MSRT, so we were further along than they were. We did 0 PT here, all range, house, vertical insertion, hook and climb.
After this we did a bunch of inhouse training until AIT. AIT was unique to the MSRT and consisted of a lot of force on force stuff and cqc. I asked to transfer at the start of this phase, as did my good buddy. We had couple highest range and PT scores, but we started to see through it and realize it wasn't for us at this point.
Man too much to type here but basically there is A LOT of time spent training, and very little operational stuff. At monthly all hands, captain said big things on the horiZon and to stay ready. Nothing ever happened. The "team" guys had a superiority complex that was unreal considering they had zero operational experience. We realized we made a mistake when for PT we were sparring and training jiu jitsu for my friend's upcoming MMA fight and we were told we had to do crossfit or lift weight as our PT like the rest of the guys.
But if training is your thing and you don't mind never applying your skills to anything but a variety of ranges, it's a sweet spot. Looking back it was an awesome job, but the egos galore killed it. Very long days for not much to show for it.
Daily routine was 7-930ish PT. 9:30- whenever range or whatever training of the day. Only thing that was consistent was PT time lol.
Now you have to be an ME rate to get there I think. But I would seriously consider what exactly you want out of it. I keep in touch with couple buddies from my green team who lateraled to ME, and both are PMs now. Went to sniper school and all that.
Sorry to ramble man, I just wish I had someone to give me this info before I went. As you probably know it's a certain personality for sure that fits in to that mold.