I got back to this project which was shelved multiple times and it's likely to be shelved again but hopefully some serious work will get done before that :)
With reviving efforts I found couple problems: original LCD appeared to be shorted, it didn't survive -10 volts on the Vee line controlling contrast. Luckily I got another from Mostek MK38P70 piggyback demo. The other problem is with my serially programmable parallel memory which I made for easy prototyping. I found out it reads out rubbish at regular 5 V but at one diode lower drop it works reliably enough. I haven't found the reason why that is yet, will have to measure around the board when I have time. Meanwhile you can look at the board there: https://easyeda.com/jan.tichavsky/ISP_FLASH_ROM-f34bf22249cc4cecb7377b1c78951f8e I believe the Gerbers aren't exactly up to date and I fixed couple close traces that did or could pose a problem. Schematics and BOM are unchanged and current though.
I want to move on from the breadboard to PCB, some initial work was done here https://easyeda.com/jan.tichavsky/Intel_4004-26742a05de344889a50cfec7e2f6f927 The plan is to have simple but somewhat complete MCS-4/MCS-40 chipset: 4004 or 4040 CPU, 4201 clock generator, plenty of 4002 RAM, 4289 standard memory interface, 4265 I/O chip, and place for 2732/2764 program memory. I will need to sort out power supply, I'm partial to vintage 723 regulator, some interface connector, and LED indicators which should be ideally through hole but those take a lot of space.