Well, I made some headway with the help of google's 3d printing tips and trick community. There are several subtleties to getting this board running, which I'll share here in case someone else comes to st.com looking for help.
My kit did not ship with a jumper. Other users have received kits that shipped with a jumper installed on J22. J22 must be installed for the kit to boot from FLASH, but it's not necessary to load the firmware as is implied in UM2067. If you know STM32 devices you could infer that from the schematic, but I am not that familiar with the product line. Also, the schematic is unfortunately omitted in UM2067. J22 needs to be installed and left in place for standalone operation.
Marlin will not operate properly if no thermistor is installed on J13-pins 3&4. It trips an error handler designed to prevent thermal runaway. If you know Marlin you might anticipate this, there is little to no information about Marlin in UM2067. If you want to test this board on the workbench without a 3D printer, you need to at least connect a 100k resistor to pins 3&4 or Marlin will shut down immediately after starting.
I never got the image to install via mass storage. The easiest way to do this IMO is to use the ST-LINK Utility (STSW-LINK004). Connect USB to J11, and use Target>Connect... and Target>Program; this may not be necessary unless you make code changes, because the board (allegedly) comes preprogrammed with a build using all the default settings. It is possible to use ST-LINK and the serial console simultaneously, which I thought was neat.
The SD card must have a /sys or /SYS directory. That directory must contain a file called M_CFG.G. The filename must be capitalized, even though this appears to conflict with the filename coded in the project. Additionally, M_CFG must not have any lines beginning with comments, and all lines in the file, particularly the last line, must be terminated with DOS-style CR/LF newlines. If there are any lines that begin with semicolons, or if the last line is not terminated with a CR/LF, Marlin will never finish parsing the file, and it will hang on startup.
The web server is not part of the SWSTM32/etc software build and is not executed by the STM32F4. The server and all html documents reside in the wireless module, and changes to the project configuration file (such as altering the SSID or WEP key) will not affect operation. This process is handled using another software tool. I have no explanation for why it is included in the configuration file, unless it's just there as a reference to the STM32 developer troubleshooting the build.
This represents about a week of part-time struggle by several users in getting this product working. I hope that it is useful to someone, and I hope it helps to alleviate the scarcity of information available online. I realize that it's an evaluation kit designed for developers of 3D printer hardware, and not a consumer printer control board, but I feel like more people overall would be attracted to ST products if it was not so challenging to get something like an evaluation kit to work out of the box.
