If the earliest you can leave is 2 pm EST, what's the latest you can leave? Do you have to be in Jefferson by a certain time?
If you leave Detroit at 3 pm EST, you'll get to the IL state line between 5:30 and 6 pm CST. At that point, you'll be heading opposite of the heaviest traffic. Yes, it will be busy, and sure, there could be a crash or three ruining the drive, in which case you're screwed. That said, if you follow the Google maps suggestion of taking I-294 to I-290 to I-90, the only two real snags should be the ramps connecting those interstates. At 6:30 pm, the traffic shouldn't be terrible.
Regarding the tolls, the Illinois Tollway system does have open road tolling for any barrier tolls, but even if you don't have I-PASS or EZ-Pass, you can still go through and pay the toll online within 7 days.
Unpaid toll info here
I have I-PASS, so I've never tried that feature. If you don't want to tempt fate, you can always pay cash at the barrier tolls. Just make sure you stay to the right to use the cash lanes.
As for the suggestions to take I-80 West to I-355, that is an option, but it always seems like traffic is bad on that stretch of I-80.
My advice: as you get closer to the Chicago area, tune in AM 780 for traffic reports on the 8s. Google Maps has you taking "the Borman", "the Tri-State", "The Ike Extension" and "the Jane Addams". Those should be mentioned in the second half of the traffic reports, as they always cover interior expressways first.
Good luck!!