Loch,
It seems you have a pretty good ear, as well as some understanding of how strings vibrate, and that your main issue is with the steel bars on your Fender. From what you're saying, it sounds like you don't generally have a problem tuning your other instruments - whether to a piano, a tuner, or just to themselves.
So - what kind of flats are you using, and have you tried, or considered, others that might be somewhat more flexible? And with the ones you currently use, are you able to accurately set the intonation?
Depending on the strings, and their age, the various harmonics may be aligned better or worse, and be more or less pronounced relative to each other. When these things aren't so good, they can confuse tuners (some more than others), as well as your ears.
Your original question about stretch tuning is perhaps more interesting, but it doesn't sound to me like that's the real issue here.