If they're very close to big birds and not used to them, it could be a problem. My guys were well established in their aviary when we introduced our TAG, who watches them daily from his gym. Most of the little guys don't seem the least bit interested in him, though the Gouldians do occasionally come to the window to check him out. But being brought into a new cage & set beside a big ol' hookbill could indeed be stressful, at least at first.
I don't know orange-cheeks, but generally your diet sounds fine. In addition to their seed mix, my guys like all kinds of veggies & fruits, and we throw in millet, thistleseed and one of the manufactured treats as well. No need to chip up the cuttlebone: they'll work on big ones. You might consider adding grit and a calcium source (we feed egg shells we've boiled/nuked).
Sure you want more finches... don't we all?
Cheers,
Pat