At Muff Wiggler I've found some hints and a circuit for transistor matching. I've built that circuit on stripboard and now can start with the transistor matching: The TTSH design uses various pairs of 2N3904 and 2N3906 transistors. These pairs should each have a very similar base-emitter voltage (within 2 mV difference).
And here we go for the matching. Measuring transistor after transistor:
All 2N3904 NPN transistors are pretty equal, with a base-emitter voltage of 615mV to 617mV. The 2N3906 PNP transistors spread a little more, from 603mV to 609mV, but many with 606mV or 607mV.