I could not think of a more IMPRACTICAL small computer chip set than the 4-bit 4004.
"Practical" in the sense that it was used in a commercial product and sold for a profit by the manufacturer. i.e. not laboratory curiosity or a secret government project.
It was so incapable Intel quickly replaced it with the 8008 and then the 8080. Date LATE 1971 and not really used much until 1974 as engineers did not know how to program.
Here in the commercial, for-profit world, the concept of a monolithic processor evolved into the 8008 and then 8080. The 4004 had a 10 year product life-span. Even today very small-scale microcontrollers are very practical for many applications. Ben Heck recently posted a video about the ATTINY10 microcontroller in a SOT-23-6 package. And Dave has been doing videos about the 3-cent Padauk PMS150C in SOP-8.
On a practical side a 20-bit microprocessor chip set that actually flew a mil-spec fighterjet in 1970 and all with the exact technology as the 4004.
http://FirstMicroprocessor.com
A very remarkable accomplishment, and well ahead of what Intel was doing. Too bad it was hidden away for so long because of government/military secrecy. Also too bad such technology was apparently unknown to NASA. The MIT-developed technology for the Apollo Guidance Computer seems pretty crude by comparison. They even used hand-woven mag core technology to store the firmware.
Your story deserves better coverage. Have you contacted the computer history people? There are many videos on YouTube covering much more mundane projects than what you are describing.
The 4004 was developed rather from the opposite end of the process. Federico Faggin had to "sell" the Intel management on making a general-purpose, programmable solution for Busicom's desk calculator. And then Intel had to buy-back the rights from Busicom in order to sell it as a general commercial product. Very interesting to hear your scenario of just pouring more money/resources on the project to meet the schedule.
Mr. Holt's video is very interesting and amazing that it is not better covered by documentary videos, etc.
https://youtu.be/aVEm5SSUULc