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.
6" Luthiers Saddle and Nut Slotting Razor Saw
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.