Balance of leg muscle usage while riding out of the saddle
I suspect your glutes are working harder than you think. Because they're big muscles, and cycling (seated) uses quite a lot of their range, but excludes the extremes, they'll be late to fatigue. This is even more the case if you do a lot of squats or leg press.
That's not to say that you can't recruit them more. When I get out of the saddle for climbs, which I don't do very much, I tend to be overgeared. That certainly seems to make them work harder; it also makes the quads work harder, but not by as much.
I reckon - and you'd have to test this - that a lower torso position while standing would help. That would suggest hoods, but with your arms bent and taking some weight on your triceps - just a little to steady you at certain points in the stroke - the vast majority still needs to go through your pedals, even more when climbing steeply. It's also going to be more aero than a more upright position in sprints. I assume standing while using the drops isn't an option. I sometimes do for short rough patches but it doesn't really work for long, for neck and wrist (brake) angles. Or maybe it would work for you.
You sound almost like you're over--using your calves. If that's true when seated and not just out of the saddle, there may be some room for tweaking.