Actually, pista bars can be sweet for fix gear climbing. I have a setup with medium deep and wide pista bars with V-brake levers. Really good for epic fix gear climbs. The huge levers are great out of the saddle handles and when I do sit down, the arc of the pista bars rotates my wrists in, elbows out and opens up my lungs. And on those epic climbs, rarely do I want to cruise on the hoods. That's the luxury of the geared crowd who can spin up hill.

My first season using this setup was when I rode the Crater Lake Cycle Oregon. I came to really appreciate it on day 6, our 4th day straight of 5000' plus. That morning started out with a 16 mile climb. Everything about the bike was perfect. (I was using a low gear - 42 X 23 - and flipped the wheel at the top of the climb. But judging from relative pedal RPMs I saw, few were using a gear that big.)

OP,for serious single speed/fix gear climbing you need several things. Great hand positions, especially out of the saddle, that allow you to pull hard without injury or chronic problems. Drop bars are a real plus. Brake levers and hoods your hands really like located on the handlebars to give a solid, comfortable position to pull from out of the saddle. (This may well not be your preferred flat ground cruise location. If that is the case, you have to decide priorities. I have two complete cockpits; bars, hoods, stems, cables and brake calipers since the levers are of different types, one set up in normal road configuration, the other as described above.)

Second is shoes, cleats and pedals. You need to be able to pull up hard on the pedals. Simple math will tell you how steep a hill you can get up in any given gear just standing on the pedals and not pulling. At a 16% grade and a 72" gear and 7" (178mm) cranks, just standing on one pedal with all your weight you can keep the bike from rolling backward. Obviously this way too tough a gear to be able to pull the pedals through the top and bottom dead spots. But if you call pull up with all your might, you can pull them through/roll through. 16% and steeper is possible IF you are strong enough to do pull on the handlebars and pedals like a full body "clean" of a "clean and jerk". I used to go up Blue Hill outside of Boston on an 81" gear. 10% average for 0.9 mile. About 150' at ~18%.

It is all possible, just hard. But you will look at the guys who reach for those big cogs and little gears as wimps after you get there.

Ben