Traditionally you have to bring his arms down by punishment as you have been doing. Some of the very old style boxers used to use a more crouched and would lean more off center bodily over to one side sort of a style.That forced the big dude to lean over and come hunting off balance and over committed;those rising 45% uppercut sort of hooks would come into play as you caught him leaning in it.

Personally I like the idea of playing all distances and disrupting their arms on your way in or on their way in, so you think in two's; bang bang off each side, tap his lead arm in or down when he reacts the opposite way, go in under it bodily so you smother his movement. Get on the inner, liver shot and over hand bomb so you are setting your feet and movement to land harder to the opening he leaves as his arm reacts to your first move, that sort of thing.