Officially these clamps are called TSO Power-Loc Bench Connector Dogbut I will affectionately pat them on the head and call them Loc-dogs.
I am a dedicated MFT style benchtop advocate and use these extensively to attach many items to my benchtop/side with them. With the tabletop’s dog holes countersunk, they have a zero top surface profile,
This blog is to reserve a spot for them in my clamp series, and my full review of them can be followed here.
As well as attaching bases/jigs, they can be adapted to low profile some workshop equipment, eg. Bessey Auto Adjust hold down clamp.
On the contrary crowie... I use them on my mini tabletop... you just need a skinny (19mm ish) tabletop. Here a re a few options available to me,
though with the last picture, the air pods can be attached direct, They just offer multiple choices and when one doesn't know the answer, with multiple choices, you have a 25% chance to guess it right.
If your first cut is too short... Take the second cut from the longer end... LBD
Petey, unfortunately they are designed to "clamp" 2 x 19mm stock... can even handle that recalcitrant 3/4" stock as well. They have a reach limit of 30-40mm.
Below that limit, I use a range of spacers cut from 6mm thick MDF to pack out underneath or some 5mm thick "up market" acrylic spacers, but being clear... too easy to lose only to find when no longer required.
In your case, you would need to counter bore the benchtop underneath the dog holes to achieve the desired thickness, Shouldn't affect the integrity of the benchtop.
If your first cut is too short... Take the second cut from the longer end... LBD