hey hey sglessner4
wow wow wow, really late during busy time during harvest season and festivals.
booking.com, trivago.com, tripadvisor.com your budget is low even though you may get lucky finding something maybe not as close.
put your dates and filters in, click map and see what is left to reserve. are you traveling by train? important to know check-in is 3-4pm check-out is 10-11am. flights out of venice (VCE) are very early, like dark early and where are you flying back to.
your plans are like many others, want to see as much as can with limited days. spending lots of time in stations, airports, train with not really enjoying the place. it's your vacation you do you. plus what attractions/activities have been booked with many being sold out. good luck, enjoy a gelato and big bowl of pasta
aloha