Suggestion would have been to install automatic drains on all your laterals and main line.

Now you should probably rent an aircompressor to do the job right. Your buddies 4 horse craftsman does not put out enough air....

I've been using a 4 HP Craftsman with a 12 gallon tank for around 10 years now without any problems (also in MA). A couple long/far away zones I'll do a second time. YMMV.

I used a portable compressor used for nail guns, etc. I did one zone at a time, 2 times. It worked fine.

My concern now is that the entire back yard is under water. How much of that will migrate into my sprinkler lines and possibly freeze up and ruin the lines?

It has been my experence that the lines will fill up if a yard is flooded.
If you have poly pipe I would not worry about it but if PVC you could have problems if you have an extremely cold winter.

I have 600 feet of 3/4 inche line to run taps on my acreage. This is black polyethelene line. In fall, I lay the standpipes down, and let them drain. My experience has been that I will lose the joint fittings if they are full of water when they freeze, but the pipe itself is fine.