I can help you guys out. Just three days ago I bought my moto 360 at your SW version and had this EXACT issue. Here is how I fixed it.
First off, do yourself a favor and delete the lastest version of Android Wear on your phone. While you're at it, be sure to get rid of Moto Connect as well if you have installed it. Basically, what is happening, is android wear 4.4 doesn't seem to be compatible with the latest version of Android Wear for Phones, so as your phone is attempting to update your watch from 4.4 to 5.1.1, it throws this error.
Step two, disconnect your Moto 360 from your phone in the Android wear menu on your phone. Factory reset your Moto 360.
Step three, go to on your phone and download that APK to a location you can find it. This is an older version of android wear.
Step four, install this APK. Reboot your phone for good measure, and connect your Moto to your phone using the version of Android wear on your phone. MAKE SURE TO NOT ALLOW ANDROID WEAR ON YOUR PHONE TO UPDATE IN THE GOOGLE PLAY STORE.
Step Five, once everything is connected, on YOUR WATCH, go to settings --> about --> software updates. This step takes a LONG TIME, around 10-20 minutes, and your watch must be over 80% to complete this. When it finishes (the green circle wraps all the way around the X) it will ask if you want to upgrade. Tell it yes. When the watch finishes and reboot, FACTORY RESET IT AGAIN.
Step Six, With the watch reset, remove android wear from your phone, and do a fresh install on the play store. Now connect your phone to your watch. You should no longer have any issues. Your watch is now running Wear 5.1.1 and your phone is running the latest AW App. Go ahead, install Motorola connect and any other apps you want to have, and most importantly, ENJOY YOUR NEW WATCH!
To any mods out there watching, I'd recommend sticking this post or something. This is an error that is going to come up a LOT until google figures out why that happens. To my knowledge, this is the ONLY way to get a 4.4w2 Moto 360 running on the latest android wear release.
---------- Post added at 10:48 PM ---------- Previous post was at 10:46 PM ----------
Check out my post just below yours. I fixed mine this way. Post #7.