I`ve managed to run the LM386 amplifier on the sound board. The problem was probably in lack of deglitching caps by power pinf of hte ICs used in the assembled version. After adding those caps, the amplifier just started to work as it should be. Hovewer, I `ve experienced some more problems with CLK signal generator. I couldn`t choose R and C values needed for proper operation. Finally I ditched the circruit and repaced it with 1Mhz crystal generator on the back of the PCB. It doesn`t look as good as the original version, but it is solid, and works perfect. All the basic functions of AY-3-8912 were checked with some simple Z80 assembler code. The amplifier, speaker and volume regulation also worked fine this time.
The actual setup for the moment, with all the components made so far: