So, you are using your own tool chain and your own version of Qt compiled with it. Nothing really to do with the Qt SDK.
I'm using the version of the Qt API that came with the SDK, I didn't recompile it.

Does it change if the files are really local?
The files really are local! =(
They are on a networked drive, but the drive is actually on the development machine I'm using. I think, because it's networked, Windows itself keeps making the path UNC instead of regular. When browsing in Windows explorer, the path shows at UNC even.

Does it change if you use the supported MingW and matching Qt in the Qt SDK?
I'll check.

Does it change if you replace backslashes '\' with forward slashes '/' in the PRO file paths?
All of them are, as far as I can tell.

Do you really have directory structure where folder names are in parentheses or square brackets?
Yeah, I use them to make my more common and static folders at the top of Windows Explorer (since brackets are sorted alphabetically before letters).

If you intend moving this to Mac or Linux then you will probably want to rethink that as these characters have special meaning to the command shell. It may even be the issue here given GNU make's UNIX pedigree (What shell will it be using?). The only place in the command you show where "d:\Jamin\" is present is immediately followed by one of your parenthetical directories.
I do intend on compiling on Mac and Linux - thanks for the heads up, I didn't know brackets and parentheses would be a problem. I'll try without them.