OP, sounds like having good restrooms and showers are a must for your camping in your van conversion. We are familiar with your van camping as we had a new custom built 1984 Chevy StarCraft Van Conversion for many years and even used it many times for our shorter travel and overnighting or a couple days long trips when we didn't want to take our TC with the truck or our 5th wheel or our Class A MH. We really enjoyed "roughing" it sometimes but at almost 75 and wife being disabled now since 1999, gave the van conversion to our daughter and we use either our TC or the 5th wheel. Sold the MH too a few years ago.
No microwave in our van conversion as we ate most main meals in restaurants or that we'd made at home and took along, However, I did install a 12,000 BTH forced air furnace in the rear of our van with the 20# tank in a hitch mounted rack outside because we like to go in cold weather too. Also had a tall 5 gal capacity flush Porta Potti on the in side behind the driver's captain chair seat. Worked great but still needed a CG with a decent shower. Porta Potti can be dumped anywhere in a toilet so no issues there!
From what you described being your likes, Grand Haven State park, Hoffmaster State Park, Ludington State Park, Petoskey State Park, and Wilderness State Park fits your bill quite well with secondary choices going to Van Buren State Park, Holland State Park (2 units), Muskegon State Park, and Silver Lake State Park and Mears State Park. Other choices too in State parks on Lake Michigan but are lacking in more than one of your mentioned desires. We have camped at every one of these many times and know the parks and the surrounding area too. Actually, have camped in all but 3 of the over 100 Michigan State Parks over the years. We are in our 52nd year of RVing and have lived in Grand Haven all our lives and wouldn't even think about moving as it's fabulous here!