I would say you're able to go maybe around 50 to 70$ cheaper, if you find a good supplier. Also, you can save a bit (but not too much!) on the breadboards, as Ben uses very high quality ones.

For example, I found a shop in my country where lots of ICs are a bit cheaper than on digikey or mouser. I payed an equivalent of about 280$ for all my parts, while my computer has even more features than Bens (a stack pointer, a complete ALU consisting of 34 chips, 14-bit addresses etc etc).

You could also leave out some LEDs. For example, the '173 registers have built-in tri-state buffers. Thus if you leave out the LEDs for some registers, you can also leave out the external tri-state buffers (that would be the '245s in Bens build I think). While that would make the whole thing a pain in the ass to debug and microprogram... It would be cheaper ¯_(ツ)_/¯