I would pay the money to switch to the flight that gets in around four, with bags you won’t be able to go thru security or easily go downtown, thru security at ord isn’t great but pre security with bags is really not going to be a fun way to spend four plus hours, go to a hotel and you are eating into the 200 you are trying to save, in the end separate tickets with luggage is always dicey because you have zero protection and limited flexibility,