If Dura-Ace is rated for 30 teeth max, it Should do 32. I would not expect it to handle 34. Your money, your choice---test it and see. If you forget what gear you are in and shift to big-big and rip the derailleur off, you will know it didn't work.
If I were you I might consider a GS derailleur and a 34- or 36-tooth-max cassette (Never looked at SRAM but I hear they are Shimano-compatible.) You might even shop for a New Old Stock 5800 GC derailleur---it will weigh a few grams more but will pretty much work the same, and if you later decide you don't need it ... take it off and save it for when you do (I doubt CarbonFiberBoy would need extra gears, but we humans will eventually.
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The other thing to do is just try different approaches to the hill. Look at it as a challenge and use different tactics.
I am serious. I used to be fit and lean with huge lungs and a heart which could pump gallons per second. Then i got fat and had heart issues (easily corrected with minor surgery.) However, when I got back on the bike, i couldn't spin up hills---heart said No---and I couldn't attack hills---or rather, i could, but i couldn't sustain the attack and would either die at the top or die trying.
Now I take hills at a slightly slower cadence, staying steady, and paying a lot of attention to breathing. I stand up every now and then for a few strokes, just to refresh my muscles. I take five-second pedaling pauses to catch my breath and rest my legs (and clear clogged blood.) I look at hills (short, sadly, and not steep) more ad middle-distance runs than sprints, where the goal is to stretch my resources all the way out to the top of the hill. it is a lot less satisfying, but at least i can get up the hills now.
And yeah, spinning is better than mashing, but ideally you shouldn't really be doing too much of either. I never mash. I simply don't have the power, nor the VO2, nor the heart capacity to mash. I would burn out every system almost immediately. But I cannot just sit and spin---I cannot breathe fast enough nor flow enough blood to keep my legs spinning, even though the load (fuel and waste) is less.
I have to vary the pace. Some riders hate variation, and prefer to set a tempo and just grind it out. Some can stand and spin a tiny gear for hours. Find which works for you.