Well, looks like there are some differing opinions here. I would still go with the higher protien feed. The calcium may or may not cause problems, but lower protien equals slower growth.
I've recently changed the feed I use because part of my flock is in heavy molt and I think the higher protien will help them out. I think I'll stick with this when I hatch chicks out in the spring as well. If you're main concern is that it is a pain to keep two different kinds of feed I'd suggest the following. Switch to a 22% gamebird mix and offer free choice oyster shells for your laying hens. This will get your pullets to point of lay sooner then the 16% layer feed, you don't have to worry about too much calcium, roos will also grow faster for the freezer (if you do that) and everybody should stay in good feather. I only switched over recently so I'm not positive about this, but they seem to be eating less of the gamebird mix as well--which is a good thing because it is more expensive.
Do keep a close eye on the chicks though because they're more likely to get cocci when they go off the medicated feed. It's easy to treat, but can kill them quickly if it's not caught right away. Good luck with your chicks.