Your definitely are looking at the right radios for your price range then. There are some cheaper lesser marketed radios that have all those features like radiolink and flysky but in general if you want more factory support and warranty coverage then the big 3 is a great place to start.

Could be somehow that the motor noise/emf is causing the bad signal. I dont think its a power issue as it sounds like everything works up close well enough and its a range issue glitch but the older analog servos especially something like a 645 could be enough of a current drain on the BEC to be a problem to somehow shorten the range.

Don't know why Spectrum says it could overheat but my guess is the frame rate on how fast that receiver will update servo position is faster then a analog servo should be updated. I think the older more compatable receivers have a slower framerate - goto page 10

https://www.horizonhobby.com/pdf/SPM5100-Manual-EN.pdf