I found confusion about the flyback's actual winding configuration. OP should double check what he's finding. Just tell us the ohmmeter readings between pins 5 thru 8.
Kortek KV-1403V flyback KFS-61202 or KFS-61202a crosses to
H.R. Diemen HR 46100 but the winding schematic is different, showing taps instead of separate windings and possibly mixing up pin 8 with pin 6? HR 46100 used for KFS61202A/KT2003V DUGO, KORTEC VS20475T, TATUNG 19"/20"TELCO VGA.
KT-1403NA also used the same flyback, that circuit includes that pin 5 is GND, and primary 1,2,3,4 daisy-chained and secondary 6,8,7 is also daisy-chained.
So the KT-1403V schematic is a bit misleading for the flyback windings.
I would double check you're using the right pinout, and the one winding 7-8 is truly open-circuit. There must be continuity between 6-8, 8-7 I think.
To remove the transformer from the board. You'd need a good solder sucker or lots of solder wick. I don't think flyback transformer open-circuits are accessible, to do surgery.
They are potted and the only place to fix a bad connection is at the underbelly at the pins, and that is too much for me.
KT-1403V repair info symptoms has some faults he found.