RE: Flying cheapest economy so I HAVE to check my bag
Is you Omaha/Chicago flight what United tickets as "Basic Economy" where cbin baggage is limited to "one persional item" and does not allow a full size carryon? It appears that United's "Basis Economy" also does not allow complementary seat assignments nor group/family seating unless you purchase advance seat assignments.
If you are limited to the one personal item, you should be able to run faster. But try to pack all of your essentials (eg medications) and a change of at least fresh socks and undergarmets.
If your group did not advance purchase seat assignments (hopefully forward near the egress door), don't wait for each other. Sprint for the departing flight with the first to arrive at the C gate to let the gate personnel know that they are four more close behind in the event that the aircraft is loading and close to door closure time.