I am generally good at research but I have no hands on experience with turning. I am honored at even the attempt to try and help you with your plight. I contacted the tool's manufacturer Robert Sorby to try and see what they could offer. One of their agents provided me with a PDF that I don't think is hosted on their site.
I have the best I could muster for the official instructions on how to use the tools you have pictured. However they don't cover your concern about the surface scratching but I have some ideas about that.
Boring Bar and Depth Stop
The tool in the middle is the boring bar and depth stop. Depth stop appears to be an adjustable collar. Pretty simple to figure that one out but here is the content of the document all the same:
The boring tool is used to remove the centre of the hollow vessel or bowl to an accurate depth. The depth stop limits the depth of cut to prevent the risk of cutting through the bottom of the project. The tool should be presented to the
work horizontally and cut on centre line. The boring bar is sharpened by rubbing a diamond file on the two cutting edges.
Hollowing Tools
The bottom tool picture is a fixed edge swan-necked hollowing tool which is designed for general cutting and hollowing. The tool above and on top is just the same except the cutting head is adjustable making it more versatile for more complex cuts and better geared for smaller sizes of work as well.
These tools cut on the centre line of the work. Throughout which the tools are held horizontal. For a more gentle cut rotate the tool until the tip trails around the 8 o'clock position. Make a series of light cuts starting from the top of the work and working towards the bottom. We recommend that these tools are honed with a diamond file on the bevel. If the tip is severely damaged it may be necessary to re-profile the tip on a bench grinder.
The following notes are also present
- Cutting occurs on centre.
- For a gentler cut rotate the tool until the tip trails up to 15° off horizontal.
- Tool must be horizontal at all times.
Wall Thickness Gauge
More of your issue comes from the Wall Thickness Gauge which is supposed to make it so you don't cut through the wood completely. It is expected that the external shape of the work is completed before these tools are used. The following is the instruction for setting the gauge which I am sure you figured out:
- Lock on to ferrule with 'T' knob (A).
- Slacken screw (B) with allen key provided.
- Holding the finger loop in contact with the handle, set to the required gap and retighten the screw
I don't know if this part is just obvious but based on what I read (it does not say itself) the bar will move while you work obviously. You will know you hit your desired depth once the bar comes to rest and is not under tension. Not the most fool proof system (assuming I understand right) but you are cutting blind so it is better than nothing.
Some notes also compliment the gauge:
This can now be left in position whilst turning if required, and can be swung in and out to check the wall thickness as you tum. If the project is made from an open grained wood such as a burr, it is best to check the wall thickness when the work is stationary.
N.B. The wall gauge can be bent if required for any difficult
areas. This is sometimes necessary on deep necked hollow
vessels.
The last note has the following accompanying photo

Scratching outer contours
Does the bar scratch all of the work or just the tighter inside contours? Perhaps you need to bend the bar more for part of the cuts? Also I cannot tell from any photos what the end of the gauge looks like. Mostly wanted to know if it had a flat or rounded end. I would have assumed the latter but it is possible either way that you have a manufacture defect?
My suggestion would be make sure that the end is rounded as much as possible. Rotary tool and using a few different heads should help. Polish that baby and that should hopefully prevent scratches.
Only other suggestion which you are probably already doing is make the outer surface slightly uniformly wider than the intended finished product and clean once you are done hollowing on the inside.
For completeness there is a warning both in this document and almost every video I watched on the subject.
All swan necked hollowing tools should be used with the straight section of the shank on the tool rest. At no time should the swan necked section of the tool come into contact with the rest.
The markup from the document was also underlined. Clearly set to stress the message