Yes, south..... but.... you can get too far south too. If I had your tag, and time to scout, this what I'd do. Scout early in the summer, June and early July, before anyone else is out moving them around.
First, I start by going south out of Loa, on the gravel road that eventually ends up in Escalante. You may begin seeing antelope as soon as you leave the farm,s south of Loa, keep working south on that main gravel road. I'd take side roads that go west of the main gravel road, check them out for 4 or 5 miles, the turn around and come back to the main gravel road again, and go south some more, then take another road gong west, go out 4 or 5 miles again, then back to the main gravel road, and go south again, repeating the south, then west, then south, then west, until you get way, way, way south of Loa. You will eventually hit heavy timber on the south and I wouldn't go any further south than those heavy thick pines.
A second place to start looking from:
About 10 miles west of Loa, on Highway 24, there is another dirt road that goes south on the Plateau, if you can't find antelope south of Loa, take that dirt road, west of Loa, off HiWay24, and work both sides of this road (both east and west), going south until you get way, way, way south again where the heavy timber starts again.
The antelope on the Parker will move a little between their summer locations and the fall hunts but not a great deal. Where you find them early will be pretty close to where you find them in the fall. But....... like all antelope, these Parker antelope get wilder than hell the minute the shooting starts and they stay way wild from the start until the snow gets too deep to get access to them. By the third day of the hunt, they will be nearly impossible to drive any where near too, if they see you first. Count on that!!!!
Use the tall knolls to spot from, there are plenty.
Also, don't over look the edges of the trees, down on the south end, they do use them for cover. I've seen plenty in those trees, but generally on the edges, they don't go in very far. Watch closely around any water holes, they do congregate around water, with a mile or two in all directions. They travel fast to water, so a mile is nothing for them to trot over for a drink. It will be hot out there.
Early morning and late evening, prime time to look. Mid-day.......... mmmm.......not so much.
DC