Feast your eyes on this: https://cpldcpu.com/2019/08/12/the-terrible-3-cent-mcu/

The HT68F001 stands out: 512 words of program flash and 16 bytes of RAM. ... can only be clocked from an internal 32 kHz oscillator. Since each instruction takes 4 cycles to execute, this results in only 8000 instructions per second!

You can still find things like an Arduino Micro that has less ROM & RAM than the lunar lander.

But finding something new slower than a 2MHz CPU is probably a challenge nowadays; even the Micro is 16MHz and can probably be overclocked a ways above that without much work or risk.

https://www.amazon.com/dp/B00AFY2S56 - not that that is necessarily the best way to buy such a system, just showing they exist.

Another related question: Is there any production software system so inefficient that it would run faster if implemented in machine language on the AGC

That's easy. The challenge would be finding something that has less than the lander, but more than zero.

Maybe whatever is found in a basic calculator?