niisaka at Tari Lari Run has developed a method for playing Mountain of Faith, Subterranean Animism, and Undefined Fantastic Object on vertically-oriented monitors.
Download the zip file at this site and extract it into the folder of the game of your choice. The game will automatically use the modified d3d9.dll file.
However, pivot functionality will only be available in fullscreen mode, and when started from an EXE file with the original Japanese name (e.g. th10.exe for Mountain of Faith). If you want to use it with a patched version, you would have to rename its executable file.
By holding Alt + an arrow key, the orientation of the picture may be changed. The menus won't look any different, but when the actual game is started, it should similar to the screenshot.
The DLL will move the game interface around to fit in a 5:4 aspect ratio and scale the game screen to match your current desktop resolution. Thus, it's recommended to set your desktop to a 5:4 resolution before starting the game. If the scaling seems to impact the game's performance, especially on older graphic chips, keep this resolution resolution as small as possible. Also, do not use the graphic card's orientation settings. This pretty much means to adjust the monitor when playing the game and change it back afterward.
There are other options in the th_pivot_custom.exe.
The first set of options is the filter. From top to bottom, it's Bilinear, Bicubic (simple) and Bicubic (corrected). Next to those options is the sharpness level. The checkbox is whether or not you can change the filter from within the game, using Alt + PageUp and PageDown.
The second set of options is the orientation - 0, 90, 180, and 270 degrees. I believe most monitors need 270 degrees for this. Again, the checkbox turns on in-game rotation, so use Alt + arrow keys to change it if needed.
The bottom left button is to uninstall (by erasing it from the registry).