So I cleared out the old Perl, and built a fresh 5.6.1 in its place. I carefully and lovingly installed most of the lower-level modules that tended to cause dependency errors for me.
And then I built GD and got the same goddamn error.
I'm fairly close to deciding that I really don't need GD as much as I thought I did, since putting my fist through the screen would be bad and that's what GD is slowly urging me to do. (At least, the little voice in my head that I've named GD. "Punch it! Ha ha ha ha!" it screams, over and over again. "You'll never get me to work! So's your mom! Up yours!")
I have to go wash some clothes, so that other human beings will still willingly interact with me.