I'm a little unsure of what you have. Is it a regular drawer, with the slides mounted on the sides at the top? Or do you have something like a spice rack, with slides on the bottom, a solid top (w/top mounted guide), and access from the sides?

It sounds like you have a drawer that basically hangs from a single slide in the middle, above the drawer, but that would put the track of the slide in your way of access.
If that's what you have, what kind of countertop do you have? If it's laminate/pressboard, just add blocking to the desired height and screw into the underside of the countertop (with screws that won't come out the top).

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1984 300TD