I don't try regularly but couldn't get it to work yesterday. I put it down to the fact that it would have been genuinely useful since I was in a tight spot and it was raining heavily. Summon never works for me in such circumstances. My car is 3G and the (Android) phone was on "H" which I think means somewhere between 3G and 4G.
In my case the app initially said it couldn't connect to the car which is never a good sign (I have "always connected" off to reduce power drain but am considering changing the setting). After restarting the app it eventually connected (I was standing in the rain, glowering at the unlocked car while it was "trying to wake the car") and it did let me initiate Summon but immediately failed without the car moving (or even making some "firing up" noises).
I read some discussion that it doesn't seem very reliable if both the car and phone are on the same WiFi network but you've already tried alternatives so that's no help either!
Anecdotally I think it may have worked better when TeslaLog was active which is why I'll be trying the "always connected" setting.
Connectivity issues aside I speculate that the car has a number of different systems which need to be roused/awake for Summon to work, whereas the app probably only needs a subset to report the car status (e.g. sometimes it reports internal temperature, sometimes not).
So in summary I've been of no help but I feel better for sharing my own frustrations
