Michigan police officers from many, but certainly not all departments, more so than in many other states, have an elitest mindset, often referred to as being "us against them". To these twisted individuals who got into their profession for all the wrong reasons, a handgun is a symbol of both authority and superiority. Regardless of the law, seeing someone else carrying openly is easily taken by these twits as a challenge to their manhood and/or authority. This is why they are known to cause trouble. In Michigan cities and counties where the police don't have this attitude issue, they treat OCers as fellow human beings, with all people being worthy of the same respect. In some states this is to be expected, in Michigan it can be a crap shoot. The good news is that most of the hard work has been done in the past several years, and few officers are any longer willing to risk their careers to unlawfully detain you, but it can still happen.
Since you have a registered pistol, but no CPL, you can carry right up to school grounds, but not on them. Due to abusive racist law from the 1920's, the registration process is a "license to carry" which expressly makes the federal gun free school zones act inapplicable to Michigan residents who own and are carrying pistols registered to them. And Michigan has no 1000 foot law, only laws about the school grounds themselves.
Recently the law was changed, and you do now need to have your registration car with you while transporting your pistol, but just for the first 30 days as the MSP puts it into their system. After that, it's not required. Do be aware however that the MSP, sheriffs departments and local PD's are known to **** up and not register your gun at times. I strongly suggest keeping the card in a safe, and copies are good too. I do not suggest carrying it after the 30 days, ever. There is no reason to. Other than while hunting, OCing as a licensed non resident, or when carrying concealed or in a car, there is no requirement to have ID because of being armed.