The “remote wasn’t extending back properly” is probably related to fluid loss from the remote circuit, so could be related to the connector – it just takes a couple of drops of oil lost to stop the remote working properly. Any sign of ‘oilyness’ on any of the hose joints is cause for concern.
The last part of the bleed needs to be done with a syringe pushing oil through the system. If you try and pull oil through the system with a syringe, it will pull the remote button in and it won’t work properly.
The ‘goes down by about 2cm, and it stays down’ is a bit odd – if air has got into the post fluid (totally separate from the remote fluid), the usual symptoms are that the post feels spongy – it compresses when you weight it, but springs back after.
Two things to check for (don’t necessarily explain the behavior, but may complicate matters):
1) Overtightened seat clamp;
2) Kinked hose.
Easiest way to eliminate these is to see if the behaviour changes if you operate the post outside the frame.