4028 will not do what he wants. It's a decoder. He wants a johnson counter, not a normal ring counter... I agree a ring counter would be much simpler, but...
And microprocessor nowadays are never overkill.
Budget for a uC solution
PIC 16F54 - $0.66
20Mhz Xtal - $0.12
LM7805 - $0.24
Budget for discrete solution
74HC299 - $0.68
74HC194 - $0.78
74HC14 - $0.47
(price of DIP parts at Digikey)
To make a really good and reliable discrete solution, he would have to spend more money as it would take more chips (I cannot see how he could do this with less than three ICs...)
Why insist on the discrete solution, so?
With one IC and less money you get a more reliable, more reproductible, easier to implement, easier to modify (while keeping the hardware the same) and smaller circuit.
I rarely tend to see microprocessors as overkill, since they are so incredibly cheap and easy to program... There's a plethora of PIC programmer circuits available on the web, that anyone with no knowledge on electronics could easily assemble.