Another thing to ponder is that there may be a distinction between a space warp drive and a time warp drive?
The former is the older tech "discovered" by Zefram Cochrane 150 years before the TOS era, the latter would be the more recent innovation that "broke the time barrier" and may be what Sarah April was talking about in TAS when she said she was the chief medical doctor on the 1st ship equipped with (time?) warp drive.
So perhaps the space warp was originally tied to impulse/fusion power, but the time warp is linked to M/A-M reactor power?
The former is the older tech "discovered" by Zefram Cochrane 150 years before the TOS era, the latter would be the more recent innovation that "broke the time barrier" and may be what Sarah April was talking about in TAS when she said she was the chief medical doctor on the 1st ship equipped with (time?) warp drive.
So perhaps the space warp was originally tied to impulse/fusion power, but the time warp is linked to M/A-M reactor power?