If both of you want the tandem riding to work but really feel that the cadence issue is the only problem that's keeping that from happening, then I'd second the advice above to change out the crank lengths. Using shorter cranks means your feet need to go around a shorter distance for each revolution, so it's easier to spin faster (higher RPMs) with the short cranks. Conversely, giving longer cranks to the person who normally spins at high RPMs will naturally slow them down since their feet will now be covering more distance with each revolution.
I certainly notice this effect when switching between some of my different bikes. The tandem has 165 mm cranks and I naturally spin faster when riding it. My touring and folding bikes have 170 mm cranks and I find that I choose a gear that gives me a little lower cadence on those. And my road bike has 175 mm cranks with the result that I tend to pick still higher gears and the lowest cadence.
OTOH, it could well be that there are a variety of other control issues behind the cadence disagreements and in that case buying new crankarms would be a waste of money and effort.