"...if you use the ABS bleed point, it's pulling fluid FROM the calipers, instead of through them."
The galleries in the calipers are such that the pistons are on a dead-end. It is impossible to "pull thru" the calipers. About the best you can do is pull the pistons "IN" removing as much fluid as possible from the calipers, then bleeding and pushing the new DOT4 back into the pistons. There is a direct connection between the bleed nipple and the brake line connection on the Brembo calipers.
I completely disassembled and cleaned my calipers after my front wheel locked up. Found crud from decomposing OEM brake lines created a "check valve" that would not allow the pressure out of the calipers. Many photos here:
https://goo.gl/photos/Fhwu1x25B1eiqVPq6