Unfortunately, there is nothing in those links that apply to Michigan, nothing in them even suggests that there is no waiting period, and all of them suggest you check your state laws for procedure.
According to the following website you may be able to shorten the waiting period from 6 months to 2 months.
Scroll down to "Waiting Period" where you will find instructions and forms:
Introduction to Divorce with Minor Children | Michigan Legal Help
I suggest you figure out how to make it a joint motion with your husband's signature as well as yours.
Frankly, if you want to get this done right, I suggest you have a lawyer do it.
Otherwise you risk getting it wrong and finding out that you've wasted a couple of months and got nowhere.
Read the following Michigan statute:
MCL 552.9f Divorce; taking of testimony; minor children; perpetuating testimony; nonresident defendant, residence of plaintiff.
No proofs or testimony shall be taken in any case for divorce until the expiration of 60 days from the time of filing the bill of complaint, except where the cause for divorce is desertion, or when the testimony is taken conditionally for the purpose of perpetuating such testimony. In every case where there are dependent minor children under the age of 18 years, no proofs or testimony shall be taken in such cases for divorce until the expiration of 6 months from the day the bill of complaint is filed.
In cases of unusual hardship or such compelling necessity as shall appeal to the conscience of the court, upon petition and proper showing, it may take testimony at any time after the expiration of 60 days from the time of filing the bill of complaint. Testimony may be taken conditionally at any time for the purpose of perpetuating such testimony.
