Can anyone tell me if there is a correct way to proceed
I don't know if the method I used on the 4 screw, 2 piece gib arrangement on my S7 is "correct" or not, but it seemed to work.
Slacken all the clamping screws (the ones you originally asked about), then tighten them just enough take up the slack without fully tightening them.
Slacken the locknuts on the adjusting grub screws & reset them as above.
I have a recollection that I disconnected the cross slide screw bracket to be able to slide the cross slide by hand to set the adjusting screws – easier to move the slide through it's full stroke & feel for slack or tight spots by hand rather than use the feed screw.
When you are getting close to a nice "feel", snug up the locknuts on the adjusting screws – feel for any changes in tightness & tweak the adjusting screws to suit. When the locknuts are quite firm & the slide is still moving freely, start to snug up the clamp screws & check for changes to tightness. When all screws & nuts are snug & the slide is still moving freely, fully tighten the clamp screws.
Screw the cross slide screw into the nut (minilmal thread showing) and refit the screw bracket to the cross slide in that position.
When you are getting close, only very small adjustments are required. You are aiming for a smooth sliding movement without binding or slackness & it takes a bit of tweaking here & there to achieve that. You will probably end up backing off the adjuster screw you started with slightly as the others are taken up. Oil up the slide before you start. Use the short end of the Allen key to apply the adjusting screw torque lightly by finger & thumb – you will not be applying much beyond the point that the screw stops moving. When you get to snugging up the locknuts, you will probably have to hold the adjusting screws with the Allen key while tightening the nut to stop the screw moving.
I just tighten the screws & locknuts by "feel" – they are only small screws, so don't need cranking down on hard. Just tight enough to stop them coming loose in operation. Diffiicult to describe "feel", as it is also to describe how much resistance to sliding motion on the slide is "just right". Sorry I can't be more precise than that.
Not something you will need to be doing that often, though. I don't think I have had to revisit mine since I went over the machine after I bought it over 20 years ago. It hasn't seen a huge amount of use since then – though that may change in a year or two – but I still don't expect to have to tweak the gibs on a regular basis.
HTH
Nigel B.