My plan for antimagic is to make a derivative of the bomb that is more intense. Figure out why it lefts the crystals alone and make it overwhelm that. It should be enough to suck up the enemy antimagic. Two antimagics meeting and neither persisting... Well, our charms would probably survive if we used sound but throwing fully-functional and stable charms into the enemy ranks seems just a bit too much for them not to espionage that. It wouldn't work that way for the same reason that lightning hurts soldiers in full-body metal armour and they can fit ballistae on boats that are as long as the ballistae are tall, but I would still feel bad about throwing good technology into the enemy and having it just vanish as soon as they touched it because game fiat.
Still, the theory really ought to work because, well, they are making a magical effect, it just isn't being triggered by our antimagic which is mostly mundane. If we can get our antimagic to recognise theirs, then ours should defeat theirs in the ensuing fight.
I suppose that they 'might' be using backup mages to blow the antimagic particles, which would have to be physical, unless they have magic-wind which would probably be noticeable once it pushes our spellcraft formations around.
*idea for later: revise firballs to make craters to mess up open ground...