Chris, you might read "Blackout" by Connie Willis. It deals with time travel back to London during the blitz. She covers the problems of wardrobe, dialect, vocabulary etc. Her " travelers" chose their time and destination which made it easy to prepare, whereas yours apparently don't have that option. Might get some ideas from that. Two observations for what it's worth: First, even though it's a fiction, people still pay close attention to small details. "Blackout" had an easy time with wardrobe because it was wartime and the people had to make do with what they could find. Small town USA would take notice any abnormalities.The second is that many of the people who post on this forum are very knowledgeable in different aspects of WWII. I am constantly amazed at the expertise regarding weapons, airplane identification, uniforms, etc. The difference between an attack and an invasion is huge and more readers than not would catch that. The correct response would have been " thanks for pointing that out".
Methink's we have another relative of Mr.Poe here who has changed mediums from video to book. Perhaps we could point him to either a Sci-Fi or writers forum to find the answers he seeks?
Coming into this late and I'm choosing to ignore the earlier heat. Why not pick Chicago as your landing zone for your three time travelers? It's on lake Michigan as you suggested, it's a huge city so opportunities to create scenarios where they might collect some period clothing is easy, and since it is a city an odd outfit might not raise the eyebrows it would in small town america. The added bonus is that the University of Chicago was the site of the early Pile-1 atomic research, and you may be able to tie that into you might time travel scenario. The research there started in early 1942, so the time doesn't like up perfectly with 7 Dec 1941, but it's close enough to massage the timeline.
I haven't seen "The Final Countdown" in years, but I remember I liked it at the time. The weather system was a unique way to account for the time travel, the paradox was was examined, Kido Butai was lucky the storm came back.