Jean, first welcome to the ACA Forums!
Are you familiar with WarmShowers? It is a reciprocal hosting group for touring cyclists only. There are several hosts in those cities so you should probably be able to ship the bike to one of them. Would probably be pretty easy to find a host to accept your boxed bike for a couple of weeks since you are not sleeping there.
You could also ship the bike to a hotel or bike shop in one of those town assuming you have the bike shop put it together for you (they will charge) or you are staying at the hotel. However, most won't want to hold it for more than a few days.
Another option to consider is to rent a car one-way, especially if you have not already booked your flights to Wisconsin and/or starting town. It would probably cost the same overall and it may not take but a day or two longer plus you would get to see more of the USA. Gas is substantially cheaper here (roughly $0.75/liter). Cars currently start at about $100/day without checking around. Just be sure NOT to rent a car at the airport but outside the airport as airport's add on a LOT of extra taxes when a $10 Uber ride could save you literally hundreds.
You could also take the train (not nearly as nice and as punctual as European trains) especially since Chicago is the main hub for Amtrak routes west of the east coast. You could have a WarmShower in Chicago or airport area hold you boxed bike and then take the train (bike still boxed) to a lot of locations. I have attached an train system map (see bottom of this post). Most interstate trains west of the east coast only run once per day at most. Some, only a few times a week. This would definitely be the cheapest if you do not require a sleeping cabin.
Unless you are a glutton for punishment, I would avoid the USA's bus companies, especially Greyhound.
A final option would be to fly directly to the starting city, drop all your gear, and then fly to Wisconsin and back to the starting city. Depending on the cities involved, this might be the least stressful way to do it and probably close to one of the cheaper options.
Out of curiosity, if you start in Dallas, in August (hottest time of year), where do you plan to ride? Dallas' temperatures average 35.5 celsius for the high and 25 for the lows in mid-August. It can easily be 40+ also. I live in Oklahoma which is very slightly cooler than Texas and I usually tour in other parts of the country/world during July and August that are cooler because it can get so hot.
Hope this helps. If you have further questions, let us know.
Tailwinds, John