Shifting on uniglide is very difficult. First you have to reach for the shift lever, which is usually on the downtube, so your hand actually comes off the handlebars, then move it forward or backwards. Move it one click for one gear, two clicks for two gears, etc.

Sorry, couldn't resist.

I've been riding uniglide for over 20 years, never had a problem shifting, even on climbs. Granted, the climbs where I'm at aren't that long or steep. I usually pick a gear and mash on up.

Aero brake levers shouldn't be a problem, although they may not pull as much cable as whatever you have on now, so you may have to adjust them more carefully.