Well, I ain't smart enough to have a credible
theory about coax length transformations.
I take the "Farm Boy" approach: 
"Throw it against the barn and see if it sticks."
Sorry, guys.  I don't have enough years or money left
to go back to college for more "learn-nin."
That's what I've got you "Smart People" for! ;-D

I typically tune the rig into a 50-Ohm non-reactive load,
then switch to a resonant antenna.  Very minor tweeks
are usually required to peak into the antenna- usually
less than a turn on the series inductance.   Changing
the feed point connection to my full-wave Delta loop,
like removing the "matching" coil of 75-ohm coax
and replacing it with a quality 2:1 balun resulted
in only minor changes in transmitter matching.

73 DE Dave AB5S