Comparing reception on the phone is not really "apples to apples" with the controller. You need to identify for certain whether the controller is really at fault, or if the problem is possibly with the camera WiFi.
If you happen to have access to a different ST10, it would be easy to see if the other controller receives the signal better.
Otherwise, you can look at your phone's WiFi connection. It should have some sort of measure of the signal strength. Older androids used "words" instead of actual signal strength, and the best signal was displayed as "very strong". I don't know how, or even if, the iPhone 6 displays signal strength. The point is, If you have weak camera WiFi showing on your phone, then the problem is likely with the camera WiFi. If you have good camera signal showing on your phone, it is likely it is a problem on the controller end.
Cross your fingers and hope it's really the controller. ST10s are easier to fix, and cheaper to replace, than the cameras.
With all that said, the information you provided above does suggest the issue will be the WiFi in the controller. IF so, the first step would be to open the st10 case, look for loose connections, disconnect everything associated with the WiFi board, plug everything back in, and give it a try.