So the whole thing works (at least one of the two prototypes) but I have to admit that I had to "cheat" because after many difficulties with a lousy design, I finally caved and added a PIC16F818... It simplifies many things but creates its own problems.
But it works.
One conclusion is : there is no simple or easy TTL/SSI/MSI chip that helps with building a decent Finite State Machine or a simple automaton. The MC14500B would require several companion chips, including some sort of PROM, which would be overkill for a simple design.
Overall, I see now why microcontrollers have emerged and are a market by themselves. Yet I wish there was a simpler, smaller solution for the trivial functions...