I found that just removing the coarse pillar / drill press type down feed handle made seeing what your doing and making any adjustments a lot easier. I’m not sure if there still available or even called the same thing today. But in North America, I have a set of what are called Ignition Wrenches. Once used on old school automotive ignition components, there much thinner in cross section than the more standard size wrenches, and those work well for these gib adjustments. If the design hasn’t changed, the second gib screw from the top is the worst one on mine for access.

But I’m unsure of how your adjusting those Z axis gib screws. Yours might be different, but mine uses Allan head set screws as the adjusters and thin locking nuts. Since the nuts play no part in the adjustments, I just back them all off a couple of rotations, adjust each of the set screws until I have the slight gib clearance I want, then use an Allan wrench on each set screw to prevent any further rotation or movement, spin each nut in with a finger tip, and do the last final tightening with the wrench. Those nuts shouldn’t be tight as the adjustments are made. So I’ve never thought anything more complex was needed. All those locking nuts do is prevent the set screws from loosening due to vibrations and hold each adjustment screw in the position there set to against the gib. Final tightening of each nut can sometimes slightly alter the adjustment, so a bit of back and forth might be needed. Compared to a tapered gib design it takes much longer to get correct, but not impossible to work with. Luckily it doesn’t need doing very often.

I could be wrong, but something also doesn’t sound right with the mounting of your dro scale and reader head. Tightening that Bristol / adjustable locking handle that’s 90 degrees to the Z axis scale movement shouldn’t show a vertical position change. Once your Z axis gib is properly adjusted, I think I’d put an indicator against the scale and check for any movement as that slide locking handle is set and released.