I had a rotator cuff problem (sounded very similar to you).
Again, coach said that my serve was technically sound...just my body disagreed!
It was the same motion I'd had as a junior and through to early adulthood when I stopped playing. Coming back to the game as a 40+ year after a long, long break, I found my body couldn't cope.
My original motion was fairly linear; left shoulder down, right shoulder over. My new motion is centred around rotating more around my trunk. The 'serve doctor' from Bolletteri's IMG camp released a couple videos on youtube worth looking at.
My serve is now as big as it ever was and I'm pain free.
Hope you get past this.