Since he is full draft - I would look into a EPSM diet. Even if he does not have EPSM (he could - that may be one of the reasons why he is having issues with gaining muscle mass and its a high likely hood since he is draft) - the diet is still wonderful for building muscle mass. For the most part it can be obtained by feeding forage and then instead of grain using alfalfa pellets and oil. While your vet and trainer are saying "no" to oil - have they actually researched EPSM in draft horses and how this diet can really help draft horses? If I were you - I would do a little research myself.
I'll look into the diet a bit and see if it's something he'll do. He has all these weird eating habits that we're still figuring out. Not sure where he learned them or picked them up.