Can they hold dinner for you and do a late dinner? I suppose they re-routed you LAX-DEN-BOS?
The closest I ever came to missing a flight was when I was trying to fly PHX-SFO. I left my conference in Scottsdale,AZ (ritzy northeast section of Phoeniz). Well we went to get on the freeway, and the entire freeway had been shut down for construction that was apparently going to take place starting that weekend. No construction crews were in sight though!
It ended p that we had to take surface streets all the way back to the airport. I lept out of the car, I begged a counter agent to print me a BP since i was past the kiosk cut-off time, I tipped (bribed?) the person at the security line to let me cut to the front, and sprinted to my gate. I was the last to board just as the lady was turning to close the jetbridge door.
There were two other people up in the aisle on the plane when I boarded both talking about how "What kind of city shuts down a freeway in advance for construction during the week?", etc.