Another way is by careful mechanical removal means. Where the faces are not dimension critical for the measurement where even extra caution is required.
So the process wound be.
For the base of the frame, a dead smooth single cut file, placed flat on the face and gently rubbed over the rust to ‘shave’ off the top layer without ‘cutting’ metal. Next, ultra fine wet and dry lubricated with WD40 or the like, supported by the file, again rubbed with the grain ( previous grinding direction ) to clean up. That in most cases will remove the rust without adversely affecting the surface.
Never do this by hand, ALWAYS support wet and dry with the file to maintain flatness and eliminate the risk of rounding or damaging the sharp edges. That’s the difference between bodge and care…..
Same approach for the barrel…
For the knurling…..
Grind a hand graver tool to match the ‘V’ of the knurling and gently ‘re-cut’ the knurling by hand to clean out the rust. Finish with a soft brass wire brush and WD 40 to clean and a hard bristle brush at the end to remove any brass residue.
That’s my ‘old skool’ means of de-rusting and I have done many concours level restorations in that way to very good effect, with care a near new appearance can be produced in many cases.
But the caveat is, that if the rust pitting is deep, it’s never going to loose the little black spots as they are too far under the original surface to be removed by such gentle means.
All the best….