OK - I think I have everybody's answers they are looking for. This is coming from a DNR official-
It is LEGAL to carry a shotgun with you while bowhunting as long as you have a valid license to do so. So, yes, you can hunt turkey with your shotgun and bowhunt for deer at the same time. You can take your shotgun along so you can go pheasant hunting as well.
It is LEGAL to carry a muzzleloader and bow during the late muzzleloader season because both are legal weapons to use. As long as you use the correct tag with the correct kill, it is legal.
The DNR official just told me that it is the DNR official's discretion as to which weapon was used to kill the animal. So, if you have a deer tagged with your bow tag, it better have been killed with your bow and not your muzzleloader.
It is ILLEGAL to carry a pistol and bow at the same time during the late muzzleleader season because there is a specific law that does not allow the use of a centerfire pistol and bow at the same time.
Does all of that make sense? I hope that answer helps the turkey hunters, pheasant hunters and deer hunters in the crowd.