Push button catches may be possible. IIRC, the drawers fit into a "box" on its side? If so, you could build out the top and bottom of the box to be flush with the drawer fronts--simply apply a horizontal (presumably) 3/4" X 3/4" horizontal strip, then shave 3/4" + 1/32" off the drawer fronts to accommodate. The catch would lock into a cutout in the box face behind this strip, which I would chisel out before applying the strip. Because you have already painted and because these strips could be subject to strong forces, I would use long screws. Even better would be inset metal plates that could be attached on the inside with vertical screws. You would have to remove the box to be able to inset the upper plate, but a trim router should make short work of it.
Installing the catch should be easy on the top drawer. To install the catch in the bottom of the bottom drawer, you would need to make a cutout in the drawer itself.
In my side-facing drawers, I have one heavy enough to require a catch. I did the equivalent of what your bottom drawer would look like. It works very well, especially because the catch can easily be opened or closed with a touch of the foot.
I'd post photos but photobucket doesn't seem to like me any more. Gotta find something else.
Just got a 'look' at the Hymer Aktiv drawer slides and push-button latches and was thinking of you . . . in that the Hymer uses 'full height' draws (defined as the top of the lower drawer being immediately adjacent to the bottom of the drawer above). They achieve this by using a narrow lateral metallic member and plate that doesn't seem to significantly block use of the full drawer height. We'll try and get some photos as we are still engineering our own Nomer-Drawer design.