Seems i figured out that the cheapest breadboards aren't best for Homebrew computer. After switching no-name transparent boards, to elegoo (cheap "branded" ones), my binary counter is able to free run way longer than half a minute. Enough for experimentation I believe. 

I decided to step aside from initial plan, and try to build circuit to avoid manual fiddling with wires on CPU startup. 

Effectively this mean I need to supply power to cpu, hold HALT/RESET lines low for at least 100ms and then bring them up. 

The simplest scheme for this would look like resistor, connection to HALT/RESET, capacitor and that's it.

The downside of scheme - two lines bounded together, so when processor will try to operate one of them it either reset or halt. I will look a bit more detailed at reset scheme in the future, but for now it'll do fine for me.