I'm not sure (unless you are the sick pax) UA necessarily has an obligation to do so because at the level of technicality of technicalities it would be a voluntary change and governed by fare rules, but I don't think it would be very hard to find an airport agent, supervisor, or if it came down to it, call center rep/supervisor to "make an exception" based on extenuating circumstances.

In my personal case I was prepared to eat the change fee and fare difference to avoid 5.5 hours of what I anticipated to be hell if that's what it absolutely came down to...