You may already have figured this out, but you should upshift two gears when you stand up, then downshift again when you sit. Makes it easier than trying to maintain the cadence you had sitting, and easier to push a higher gear, at least for a while, when you are standing. Generally even 10 or 20 cranks standing up rejuvenates me enough to sit again, although if things are really steep I stand more.
pay attention to form when you stand - if you move your hips closer to the handlebars, that shifts some of the effort to different parts of the quads than when sitting.
Aha, who knew...
I've been trying different variations of things -- body position, cadence, pedaling style, gearing. Very slowly getting a little better.