The blog says, "simple things like swapping HC series logic for AHCT series logic", which suggests that they aren't using TTL at all; the 74HC series and the 74AHCT series are both CMOS, not TTL. I haven't built a CPU from discrete logic like this, but I would also use CMOS rather than TTL. CMOS gives you infinite fanout, less ground bounce, symmetric drive strength, lower power, less sensitive to power supply tolerances. And it's much easier to get nowadays, and comes in small, convenient surface mount packages. The drawbacks are that with CMOS you need to tie unused inputs to a power rail rather than leaving them floating, and it's easier to blow it up with ESD.

I also wouldn't use a TTL-compatible family like the 74AHCT family, because another advantage of CMOS is that you have better noise margins, and the TTL-compatible families sacrifice that in order to gain compatibility with a logic family you aren't using because it's been obsolete for 40 years.

I mean, TTL is not entirely out of production. Digi-Key seems to still have 280 TTL discrete gate SKUs in stock https://www.digikey.com/en/products/filter/gates-and-inverte..., of which the most popular is the 74LS86 quad XOR, with 20,494 units in stock: https://www.digikey.com/en/products/detail/texas-instruments.... It's even a surface-mount package. By contrast, in the same category, they have 3,394 CMOS SKUs in stock by my search https://www.digikey.com/en/products/filter/gates-and-inverte... of which the most popular is a 74LVC1G08, a single AND gate with 864,000 units in stock: https://www.digikey.com/en/products/detail/nexperia-usa-inc/....

A lot of the old TTL parts that would be most appealing for this kind of thing, like the 74(S/LS/ALS/F)181, are long obsolete, with no direct CMOS replacement, though Rochester will happily sell them to you at $640-toilet-seat prices if you need them to repair a 50-year-old guided missile or something. But maybe something like a 74LVC1G97 or 74LVC1G57 could be a partial substitute, or something like one or more CD4051s in front of a nice 74HC164? Or a CPLD? How about a CPLD? GALs/PALs are probably why the 74181 doesn't exist nowadays.

If you do want to build a CPU out of logic gates, maybe start with RTL simulation, then an FPGA, then maybe CPLDs, before pulling the trigger on a fully discrete logic design. That way, you aren't debugging your assembler, your RTL, your timing, and your signal integrity problems at the same time. That way it's more like a term project than your life's work.

If you design the boards, you can outsource the assembly to a pick-and-place machine; https://dernocua.github.io/notes/pick-and-place.html has my notes from 4 years ago about that. It elaborates a bit on the 74164+4051 plan mentioned above.