From what I have seen there is no harm in promoting young players to higher levels with better coaches, even the big leagues. As long as they get enough playing time, they grow nicely. 'Enough' playing time is not the same is maxing out their playing time, since platooning is often very effective, and I would always advise against playing guys who are exhausted.
MOST RELIABLE PROSPECT DEVO STRATEGY: END OF SEASON PROMOTIONS. Mid-season promotions might accelerate a single development cycle for a player, but it's hard to milk this into any reliable acceleration of their development. However, there's one time when you know you're getting the prospect an extra devo cycle, and that's after the regular season has ended. Player with 4 regular season cycles? Promote them during or (my preference) after the playoffs, and they get the 5th cycle. Player with 5 regular season cycles (or more)? Promote them too, and often they get a 6th cycle.
With a few elite prospects, I have promoted the player to keep playing in the playoffs of a higher level team (e.g. HiA to AA), which yielded a productive devo cycle. 2 or 3 playoff rounds later, with the playoffs over, I promoted again, and there occurred another devo cycle with a ratings bump. Two ratings bumps from end-of-season promotions is nothing to sneeze at.
I apply this strategy across my whole farm system, and my back-of-the-envelope guesstimate is that it gets ML-worthy prospects ready for the bigs 1/2 a season or even a full season earlier. This hopefully gets players well on track to reach their ceilings, and even if they are not, young prospects developing faster are more tantalizing trade chips…