"backyard of an empty house we rented" would make me more concerned than some of the other things. Granted, you'll be there on weekends, but your routine could easily be noticed. Probably should let the neighbors on either side know what's what and have your contact # and also the local police. Ours are wonderful about running extra patrol through our neighborhood when we're gone.
You might try putting a lamp on a timer and changing times each weekend before you leave...makes it look like someone's home. Might also ask a neighbor to park one of their cars in the driveway from time to time.
Other than security, sounds like you've got it covered. We had a rental house ONCE and we spent 4 months going every weekend, sometimes taking off work on Fridays too. Thought we were going to die before we had it ready to sell. Rental property is not for sissies. Good luck.