Hey Bill. Im glad you asked. Its a bit of a pet 'bone' of mine. The join you described is the best one IMHO, only the terminology needs to be adjusted.
If you are over flying at 500 ft and 'joining mid downwind, you are actually joining mid field xwind, which is IMHO the safest place to join a cct.
Joining the cct means, where you enter the cct.
So for instance, joining downwind would mean from the 'live side, either on a 45 deg, or a long downwind as you described.
But over flying at 500ft, technically you are already in the cct the moment you enter the live side, which in your example is midfield xwind.
It might sound like semantics, but your call of "joining downwind, would not be correct, and would have people looking for you in a different area of the cct. However, the call of 'joining mid field xwind' would be the correct call.