The governor controls the up shifts in conjuction with the modulator to a point. The kickdown cable takes over at WOT to carry the shifts beyond the governer/modulator cross over, as well as force a down shift at slower speeds.
Other than WOT, upshifts occur when governer pressure crosses modulator pressure. You can raise upshifts by raising modulator pressure, making the governer go higher to match it. This is done by screwing the modulator adjuster in. This is more minor adjustment 4 to 6 mph.
GM made governers with several weight combos in them. The heavier the lower the shifts the lighter ones had a higher shift. Going from the heaviest to lightest can make close to 15mph difference. If more is needed you can do a governer weight kit, or you can get a governer from a 700R4 corvette/police unit. They are the same as a 350, but the weight package is the lightest of all GM governers.