I`m in the UK so I can`t comment on Nutriphase. Hamster foods in general are `okay` for mice, but you would be better with a mix that`s full of different grains. As many as posible. Rat mix is better than hamster mix, but I`m not familiar with rat foods in the US. You can still add the bird seed loose and the bread and puffed rice though. Porridge oats dry are a favourite and you should be able to buy a packet of oats in any human food store or supermarket over there. Just plain oats, nothing with salt or sugar added or flavourings. The plainer, the better.
If you can check out some rabbit mixes over there that are not full of `fillers` like alfalfa and locust beans, look for a rabbit mix that contains mostly grains and extruded biscuits. You could add this to a rat mix and give them plenty more variety?
If you place two food dishes in their cage rather than one, it will allow them both to feed. Scatter feeding is also a good idea. Same goes for water bottles. Always have two.