There is a trick with this that might work, it's borrowed from one of the lord of the rings effects. The hobbit on the cart with gandalf was achieved 'in camera'. That is, the smaller hobbit and the larger wizard were in fact two full size adults sitting on the same rig. The principle is simple, objects closer to camera appear bigger.
Now, because Antics has not got a depth of field (that is there is no focus) the objects further from camera appear smaller than those up close without focus giving it away. In this way you can have characters running away from a giant by positioning the characters at different distance from camera. It's a limited approach though. The idea is also helped by scaling prop items in the background and foreground so that the characters appear a set size. It really works for a side shot. In theory you could force this perspective from a top shot also, like from the giants' pov. Just use transparent floor textures on the giants floor, lower the little people's room untile the are, well, little! (further from camera) I think scaling buildings down when showing the size of the giant would help a lot, also run the slow the movements down slightly to give the giant weight. Have fun, and let me know how you get on.