To hold up the ab/back pieces, I have regular nylon strapping and a couple of snap buckles on mine.
Here you can see the shorter straps with the "male" side of the buckle attached to the ab plate, and the longer straps with the "female" side attached to the back. All of the strapping is riveted to the armor.
A closer shot of the male side, which is also where adjustments are made if you need to lengthen or shorten anything.
And finally, a quick shot of both ends nearly snapped together. When I actually wear the armor, I cross the back straps behind my neck like suspenders and snap them together in the front.
All of my other armor bits have elastic strapping on them for more range of motion. My chest/back armor, shoulder bells, and bicep pieces are all permanently attached to each other too, so I can just pull the whole thing on and off like a shirt.
There are many ways to accomplish this, it just depends on what you prefer and how much work you want to put into it.