Good find @EdS - Kevin has made a very good looking recreation of the 1967 machine.
As I recall it used serial arithmetic to keep the transistor count down, and minimised the number of registers - again to keep transistor costs down. The original article includes the diagrams of each discrete logic gate used and sets out the costs in shillings and old pence. For the amateur constructor, this would still have been quite an expensive undertaking.
The gates are created using resistor-transistor logic RTL, using diodes wherever possible to create AND and OR functions. Flip-flops used an unusual “pulse” logic, where a short pulse could be introduced via a small value capacitor to set or reset the flip-flop. Whilst these techniques may seem a bit unusual these days, they were extensively used in the mid-1960s machines (eg PDP-8) to reduce transistor count.
I see that in 1967, even a factory reject germanium transistor was being sold for 9 old pence. 400 of these would cost £15, at a time when £20 was the average weekly wage.
A further complication was the design used neon indicators on the front panel (LEDs had yet to be developed). These needed high voltage (60V) switching transistors, which not only were twice the cost, but their high voltage supply could be a disaster waiting to happen for those constructing on stripboard.
It will be interesting to see how Kevin has implemented the logic design, whether a faithful replication of the RTL and pulse logic, or opted for a more reliable DTL nand gate design - and effectively reduced all the logic to nands.
Unfortunately any form of storage memory was prohibitively expensive, but the original author mentioned that he was considering some form of diode array in a jackplug matrix - and with hindsight this may well have been practical for a stored program ROM. RAM could have been created in the form of additional chains of shift registers but this would probably have been beyond the budget.
For a more recent discrete transistor computer there is the LCPU - a recent project in Hackaday.io by Tim Boscke.
This uses diode transistor logic, but with the novel innovation of using an LED in the base drive circuit rather than a pair of diodes in series. Not only does this provide a neat solution to improving the noise immunity of the gate, but the LED illuminates when the gate is activated.
