CTRL-V enters block selection mode (allowing you to select rectangular blocks of text). In gvim this conflicts with Windows’ paste shortcut, so you can use CTRL-Q instead.
Unfortunately, CTRL-Q [G] doesn’t do what you’d like since the [G] motion moves linearly through the file, so you still need to rely on a using a counted [j] motion. You can avoid having to know exactly how big the file is by using an obscenely large count, like 9999. So the full command is CTRL-Q [9999j].
Alas I don’t know of way that will avoid the ugly count hack offhand.
EDIT: Oh, I read your question too fast and missed that you already mentioned that you new about the visual block mode. I guess this is a pretty useless answer, then, sorry!