Instead of disabling wifi, have you tried actually disabling bluetooth instead? If you're on a stable wifi connection, you can do everything just as well as over wifi as you could with bluetooth -- but without the horrible, nightmarish, unpredictable, confusing, and painfully intermittent bluetooth connection problems that plague everyone using iPhones and other Apple products.
So, try a very simple experiment for me, please: leaving everything else as you have it, making sure your iPhone is nicely connected to wifi (i.e., while at home on your couch), simply slide the control panel up from the bottom of your locked iPhone. Click the bluetooth icon so it goes off (or turn bluetooth off in the settings panel on your iPhone).
Then wait about 10 seconds to make sure the watch is now using wifi. Test various features of the watch -- you'll see they all still work (Siri, receiving/making phone calls with your watch, getting notifications, etc.). Now, once you see the light (that everything still works great without bluetooth, that evil and horrible nightmare of a broken Apple stack), I bet magically you'll notice non-intermittent 100% perfect "handoff' functionality. (At least, insofar as handoff is ever functional.)
Please let us know if that fixes it for you. I'd be really curious. I think this is a big issue and everyone needs to understand how broken bluetooth is, and stop using it except when roaming outside home or office where you have a stable connection to wifi.
Steve