The tighter the cable the higher/ longer the range before shifting.
Haynes has a good explanation of how to adjust the cable. You'll need
to take measurements of the cable stopper at full throttle (something
mashing the pedal while the engine is off) and another measurement of
it at rest.

Otherwise, you may need to trial and error by tightening your cable
slightly to see if that extends your range.

If the problem really is the cable adjustment, you want to adjust in the
direction that loosens the cable. But they rarely come out of adjustment.
Check to see if the cable is hanging up by opening the throttle all the way
and slowly returning the throttle to idle (engine off, of course!). Watch
the cable to see if the tension is lost anytime. Lubrication with graphite -
I like the type that has a kerosene carrier like Lock-ease - is best.

The proper adjustment is 0.25 mm to 1.0 mm between the stop and the sleeve
at the top end of the cable. If the kickdown is still too early, look into
the engine power instead. Often the kickdown occurs because the throttle has
to be opened more than it should to produce the needed power. Mostly I've
seen that cause the lower gears to hang in too long.

Mike