General Radio could order mica capacitors with close tolerances made to their specific values.
If you want to proceed along these lines, you need to obtain a good LCR meter (such as the DE5000, much discussed on this forum). Purchase standard-value C0G/NP0 capacitors lower than the required value and measure them. Also purchase lower-value units and carefully measure them. To make 267 pF, for example, start with 220 or 240 pF, and add maybe 47 or 27 pF, depending on what you measure, in parallel. For many such circuits, the match between two capacitors is more important than the value itself (e.g., shoot for 0.2% match between 1% values). The cost of the extra capacitors will be much less than the DE5000, which is roughly $100. To be authentic, you could stick with silver mica, but they are now expensive and rare compared with the C0G ceramics which are cheap and plentiful.
Old corollary to Murphy's Law: self-starting oscillators won't.