After my experience 4-5 years ago missing my booked #8 to #30 by 3 hours, I swore I'd never do it again. And haven't. So now I always take the 'shortcut' home to Springfield MA and settle in to my personal most hated train...the Lakeshore Ltd (long, long story, but not here). Why did I book my homeward trip on the CL as I have a number of times? Because roomettes on the CL used to be about $100 or MORE cheaper than the LSL. Last time I looked, they still were.
I missed #6 to #50 as well a number of years ago. But fortunately, they bused me and more than a dozen others to IND to meet our Cardinal.
So these days, I'd find a good place in CHI to overnight. My usual trick for overnights in a city is simply Google 'Chicago Hotels' for example, and go from there. My other requirement for an overnight is that it's affordable AND within a block of mass transit other than buses.
In your situation, I'd consider booking the LSL to NYP, and spending a night there...or someplace like NWK where there's a less costly hotel connected by a walkway to the Newark station. I can't remember the name, but others have stated it's OK.
Then again, you might want to 'go for it' and hope everything connects OK. The hope would be that in the event of a misconnect, Amtrak would not only pick up the tab for a hotel but also have a roomette available on the next days' train...and on a day later Silver train. Of course, next day roomette availability during summer would be unlikely, and maybe better in spring or fall. Winter is likely to be affected by reduced consists. Also, don't forget that arriving a day later would leave you holding the bag for the first night of a guaranteed reservation at a hotel, and possibly cancellation of your hotel and car rental.
In my younger days, I'd 'go for it'. But that was in the late 70s and early 80s and Amtrak ran a lot closer to on time than today. These days, I want a 'sure thing' all booked ahead of time even though I'm retired and can lose a day with little consequence.
And if you DO discover you'll miss a connection, check with the conductor first to verify the connection will be missed. THEN get on the phone to Amtrak and tell them what's about to happen. You want to be the FIRST one to catch any available sleeper space on tomorrows train! The only problem with that is the people on the phone at Amtrak don't have a clue what is about to 'go down' with missed connections, etc. I did that several years ago when #29 from WAS was cancelled to PGH account a CSX derailment in suburban WAS. I told the agent I wanted to switch to the Pennsylvanian and connect at PGH. It took some convincing, but I avoided a bus ride WAS-PGH.