A video or article with pictures for your recommended pre-throwing stretches would be appreciated, and I know you said that's in the plans. I see so many people walk from the car to the first tee, then throw with bad form and all their effort...I'm not surprised there are lots of people with muscle strains and other pain.
That's one thing that's in the works for sure. The interesting thing in sports performance research is that there are so many opinions right now about what you should or shouldn't do before activity. I ran track in college and they would tell us not to do any static stretches before running. If you think of your muscles as a rubber band, you actually want it to have some tension so it has more stored power (you can shoot the rubber band farther - run faster - throw discs farther etc.) If you do too much static stretching you lose that stored power and have a decrease in performance but you get the benefit of the rubber band being less likely to snap.
I think the key to any good warm-up routine is getting your muscles ready for action while practicing a sport specific skill that you'll be using during your event. I ran hurdles in track and we'd do hip mobility drills followed by actually running sets of hurdles. There wasn't ever really just sitting and stretching before a race, that always happened after practice or after a track meet as a cool-down.
Off the top of my head, a good warm-up could be something like:
Start with dynamic warm-up (arm circles, twists, etc. Not too much static stretch and hold at this point, static stretches are better after rounds)
Play catch with a buddy about 50 ft apart just to get the muscles moving. Unload your bag doing some 100-150ft approaches. Throw a variety of shots too; land some flat, throw some spike hyzers, a couple anhyzers, forehands, see what the wind is doing etc. Anything you might use during the round. Step up to 200ft approaches and do the same thing. Throw some 300ft drives. Throw some max distance drives. Then go practice putting after everything is loosened up and you'll probably be more consistent than if you started with putting practice when your muscles are cold.
This warms up all your throwing muscles, helps you range in your approach shots, gets your body ready for all the shots it's going to have to throw and hopefully builds a little confidence through the putting game too.