If you want them to sound like trumpet players, have them play trumpet mouthpieces for three months.
If like horn players, have them use horn mouthpieces and adapters.
If you have trumpet players playing mello, have them use mello/trumpet mouthpieces.
This CAN be overcome, especially if you have dedicated horn players who practice, but the fact is that you'll be holding at least SOME of your kids back.
A "larger" trumpet mouthpiece is in fact the opposite of a horn mouthpiece. The largest horn mouthpiece is smaller rimmed than the smallest trumpet mouthpiece. The deepest trumpet cup is much much shallower than the shallowest horn mouthpiece.
An alternative if you insist upon using trumpet-style mouthpieces is to pick up some authentic cornet mouthpieces - you'll get a sound somewhere in the middle - but there's not a lot of sense in spending hundreds of dollars for something that's not used for 75% of the school year.