Bisected the issue. It is introduced by !1257 (merged), although in a more powerful form, where booting into the main menu with opengl and fullscreen and switching to software will immediately result in a black screen. !1264 (merged) then changes the bug into the form it currently is in.
This line appears to be related to the issue, removing it causes the issue to stop happening when testing with the steps I've been using:
Start SRB2 in OpenGL mode and fullscreen already enabled
Switch to Software mode from the video settings menu, close menus
devmode 1 and map 1 in console
Before removing the line, at this point the screen becomes and stays black after fading to black and showing the "Speeding off to level" message.
After removing the line, at this point the level loads normally without the screen staying black.
Of course removing that line is not a solution, since it would likely break things, but I don't have enough knowledge of the internals to suggest any full solutions at this point. I thought that this might be a helpful starting point for others looking into this.