Adrian’s advice seems based on the rack being steel. My interpretation of the tidy-looking steel pinion and the knackered rack does not support that idea. If the rack is brass, heating to dull red will aneal, and soften, and quite likely weaken, the already suffering rack.
Picking up some thread queries, it is a brass rack soldered and pinned to a solid brass triangular bar. With no engineering tools or expertise at all the suggested possible routes with basic tools are appreciated.
Will now not attempt to desolder as would be first time trying the technique with a torch and heating a bar to required heat with unknown solder melting point will avoid as would also need to try and pull bar away from pins at same time.
So best option being considered with a limited skills set at present is using a luthier saw 0.3 mm thick to improve the clogged notches ca. 0.4 mm wide. Strips of emery paper of a fine grade may improve the teeth profiles of others with burrs.
Having a couple of sets of needle files would make restoring the teeth easier. Why two sets? Well, a lot of the shapes can be stoned or rubbed on wet and dry paper to remove teeth from one side which makes them easier to use when only one direction of cut is vital. Having two of each shape means that modifying one does not burn your boats.
A possible alternative I would suggest is to try polymer clay. If a box (mold) is made the size of the rack and packed with polymer clay them the pinion is rolled over, the clay it should be possible to imprint the rack form which, after backing in the oven, should be quite serviceable.
Agree that needle files may give more control than a saw. Would be interested in a source of needle files that go down to the notch width of 0.4 mm and below.
The standard set of needle files that have, the Draper / CK type sets, the tapered round file minimum is double that required at 0.8 mm. The flat file is 1.5 mm thick.
Im a bit concerned that the links to rack suppliers seem to be taking you down the route of metric involute, surely your rack would be CP form like a bishops hat form?
Decided not to try and replace the rack after reading what may be involved to remove rack from a large brass support bar with no experience of this type of desoldering / resoldering. Will try and recut the rack in situ.
Just bought a 0.3 mm thick luthier’s saw which is a perfect snug fit in the good teeth slots. Learnt that a luthier’s saw has teeth same width as blade unlike a typical craft saw that own with same blade thickness but teeth actually 0.6 mm.
Luthier’s also use very fine nut files to make grooves for the strings so good value ultra fine needle type files. Smallest 0.4 mm actual slot width so could round out if needed. Less than a tenner these.
Thanks for all the comments and suggesting different approaches.