Many, many thanks to all who replied! We had a nightmare of a trip, but it was a "first world" nightmare. When I posted our question we had been (nail bitingly) standby rerouted from Boston through Dublin (although at first we were told it was through DUBAI!),then Amsterdam, where we had a 5 hour layover. We had been without sleep for nearly 24 hours and were "running on empty." Your suggestions were really helpful and made us feel less bewildered, especially Sam's.
Rather than look for a pay for a hotel in Rome, given that we were paying for a room in Venice, we took the night train, buying 2 "couchette" tickets. It was a yucky train--not the beautiful fast train we had envisioned, and it turned out we were sharing our couchette with two guys (one kind of scuzzy-looking one who spent the night drinking lemoncello--he did offer me a swig!). My 65 year old husband took the top bunk so I wouldn't have to climb up and down, but it was in many ways the low point of a pretty awful trip.
Anyway, we survived and were rewarded by arriving to a dark,very quiet Ferrovia in Venice, and then watching the sun slowly bring the beautiful city into the new day. Only later did we realize how special that quiet vaparetto ride and walk to the hotel through empty streets was!
And we have a great story to tell now that we're home. THANK YOU ALL AGAIN! This forum ROCKS!