The latest:
Day before yestrerday, I took my laptop and my wireless modem to the Sprint store. Using my hardware, they were able to get a 4G connection, and far better (though still abysmal) speeds at 3G.
They checked a map and confirmed that I should get 4G from my home, installed the latest version of the connection software, reset my modem, then sent me home.
From home, still no 4G network found. the 3G speed was marginally better.
When I called and told them, they opened a sevice ticket so that some other Sprint people, with access to better tools. they asked me to call those folks and complain, as that would escalate the issue.
I called the number and left a message.
The next day (yesterday) the higher-up tech guy called me and walked me through some debugging. No progress was made, but he told me that he had access to a more detailed map of the coverage, which showed that our apartment was right on the border of getting 4G coverage. He also scheduled tower techies to come and examine the towers in our area, to see if the hardware is functioning properly. They will call me when they finish, and the ticket will not be closed until I confirm that all is working acceptably.