My machine setup took a little time, I don’t think any of the steel components were free from warp. But I was able to get it to what I’d consider quite satisfactory without shimming, but barely.
Admittedly, I went about my setup in a silly manner. First I established a laser datum, set the table, then the Shapeoko base(a level would work, and a machinist bubble even better). Unnecessary, but its nice for visual interpretation. And It never hurts to start building a home square and plumb.
I then roughly set out the machine with 123 blocks and a suitable shim as required. In such instances, I pick a side. That is to say, most basic hardware scenarios allow some play in one direction or another, pick an applicable direction to take up that play and follow suit throughout assembly.
Using the 123 blocks at machine corners, I positioned both Y extrusions parallel to the base. The X axis was used for Y to Y spacing. Same procedure for X extrusion. I then used the 123 blocks to square the router mount to the base.
At this point I ran a program to surface the spoil board. After surfacing I used a tool similar to yours to fine tune. Noting my previous decision regarding extrusion placement, I picked two opposing screws on the X gantry to act as a hinge, loosened the other six, and corrected for north and south. Tighten screws back up. For East and West, I used the router mount. Mine doesn’t have any of the easy tram stuff, so I tighten it just enough to prevent movement after positioning. I set position, then disassembled, and tightened everything up. Once tightened, things will change. Take note of how, and adjust further. Sometimes you need to ream a few holes to eek out a little love.
Couldn’t tell you if that’s the right way to go about it, but it worked for me. Years ago I ran a large industrial CNC shop. Mind you, I ran the place, I didn’t(don’t) know shit about running or fixing a machine, there were professionals for that. But I’d call up the manufacturer, and they’d fly some dude in from Germany and the like. And to my memory, that’s what they’d do. Starting at the base, and using little bubbles, spacers, gadgets, and widgets, they’d end up at the top.