Have you looked at making a guide template with built-in stops?
Chain-drill and smooth a slot (red) the width of a Dremel bit shaft through some MDF and attach stops. (gray)
Use a #194 bit along with the attachment you showed above.

Set the Y-axis of the guide (blue) by putting the bit into position 2 of the template (Dremel switched off) and dropping it into the existing groove -- ensure that position 2 of the template matches the existing groove across the length of the guide. (Use position 3 if you need the guide on the other side)
Set the X-axis of the template by putting the bit into position 1 of the template (Dremel switched off), dropping it into the existing groove, and clamping the template in place.
Trace through the template in numerical order.
If the template pattern is the right size, the bit will be in the existing slots at each numbered position, allowing you to switch the Dremel off when raising/lowering the cutting part of the bit through the template slot at the start and end of each stone block.

Scott
EDIT: Change to the template shown below -- extended the top and bottom gray pieces so you can clamp them to the blue piece as shown.