I can easily improve my NP/HR by doing very short, very hard intervals but getting my average power/HR up is an whole other story and by feel I feel strongest when the latter was higher
I think we are all here because we dread FTP tests and want a different way to determine FTP without some form of all out test 
I used to think that Efficiency was a good guide but have come to the conclusion that for me it is as dependent on the route as my fitness. If you ride a lot of short but quite steep climbs then NP is suspect, and HR lag also has an effect. Just a note to say be cautious in over interpreting it. Maybe if you ride flat or long hills it will make sense.