But that's the problem! I AM following every set of instructions I can find! The rim simply isn't obeying!

I'm sure I must be doing SOMETHING wrong, but I am absolutely not turning the wrong way (since I'm using the heads of the nipples, on the outside of the rim, very challenging to mess that up). The spokes that need to be tightened to pull the rim back into shape are as tight as they can possibly be and the other side is loose!

Thanks for the response! I'll read through the Park Tools guide and see if it enlightens me to anything new.