Those Peoria ordinances were published April 2012, right before the state got concealed carry(not up to date). Also, no need to unload and move to the trunk when you exit the vehicle.
From here:
https://isp.illinois.gov/StaticFiles/docs/FSB/General%20Information/1-154%20-%20Transporting%20Your%20Firearm.pdfA non-resident who has a valid Concealed
Carry License from their home state may carry
a concealed firearm within a vehicle traveling
through Illinois. If the non-resident leaves
the vehicle unattended, the firearm must be
stored concealed in a case inside the locked
vehicle or locked container within the vehicle
out of plain view. For the purpose of subsection
430 ILCS 66/65(b), a “case” includes a glove
compartment or console that completely
encloses the concealed firearm or ammunition,
the trunk of the vehicle, or a firearm carrying
box, shipping box, or other container.
If you remove the firearm from the vehicle then it's supposed to be unloaded and in a case(carrying it to your motel room, etc). Hope that helps.
Also, if you're staying near Peoria consider Morton. It's a quick drive to Peoria and has several motels/restaurants with easy access to I-74/155/474.