I didn't have any luck with the official Uzbek e-visa portal, so I paid the extra $20 to have my single-entry visa processed by ivisa.com. It was ready in 4 days, and they even accepted my iPhone selfie for the passport photo.
On the border: I crossed into Uzbekistan from Kazakhstan on March 21 through a crossing designated for specific transport providers (I took a bus run by KazNetworkBus), so the only people in line were those from my bus. The border agents didn't seem to know what to do with my e-visa at first, but I had printed out a hard copy just in case, which seemed to help. I crossed over with no issues.
Coming back: I crossed back into Kazakhstan on March 24 through the same point. Again, those on my bus were the only ones in line. I wasn't expecting that I needed a hard copy of my e-visa to exit the country (which of course isn't the case but the border agents think it is). They were quite rude and yelled at me, asking where my e-visa was. I kept answering that the visa was electronic, so it should be in their system, but they wouldn't let me through until I dug through my belongings and finally found the crumpled up copy I had used to enter a few days before.
Moral of the story — print your e-visa and don't throw it away until you've exited the country.