Well, once a month is fine…From what I read of your initial post, I just assumed it was a staple, sorry. As far as the toad spitting it up, is it soft or the dry food? I would think if it’s dry and hard, the toad isn’t expecting that, and spits it out. Even the dry dog food you add water to may not be soaked all the way through and the first hard piece of food the toad encounters he doesn’t want anything to do with it.
Good question on the cooked meat/ham….Over all the years of keeping carnivorous reptiles I’ve never given them cooked meat, or for that matter raw meat. Maybe someone else has had experience with that, I certainly don't.

Good luck, let us know how you do with your toad.

Lloyd