Is it a 3x3 or 6-in-line headstock?
If it's 6-in-line, the Schallers or Planet Waves should fit, like you said. If it's 3x3 the Schallers should fit, but the PWs won't - the screw tab is in a straight line under the tuner (like Grovers), not at an angle like you described.
The other potential problem with the PWs is that they need a 10mm hole all the way through the headstock - the Variax may already be drilled like that, but on some guitars (e.g. Fenders) they have a 10mm hole at the back of the headstock but a smaller hole at the front.
I'd recommend Gotoh Magnum Locks - they'll definitely fit, and they don't add any extra weight. The Schallers weigh a ton!
http://www.allparts.uk.com/gotoh-locking-tuning-keys-p-2967.html?p=product
