You asked,

"When you say any one MCU would be better, would that take into account that the second of the small MCUs would be shut-down after startup?"

and I'd say that's still up in the air. If you have a way of completely powering the thing down, then, not necessarily. However, IF (and it's a big IF) you can find a "prototypable" MCU with enough pins at a coarse enough pitch that you can (A) meet all your requirements, and (B) see well enough to solder to the pins or do whatever else you might have to do to connect the thing to the rest of your circuitry, then that might be the path for you.

The 4000-series CMOS solution to your switch scanning issue, as recommended by Charles Bannister is workable and VERY stingy with power. If you power-down or idle your MCU each time a button is pushed, at least for a short time, and operate it as slowly as you can afford, perhaps in the 100 KHz range, you won't use much power. There's timing that you can do with other external logic that will let your MCU sleep, but, you have to trade off the cost of the extra logic + board space, against pins, however you get them.

You go on,
"My proposed development is as follows:
-- develop by trial and error on the PJRC 8052 board with an attached plug-in breadboard (0.100" spacing). I would not be using the 82C55 I/O Chips."

I'm not one who believes using those is a deadly sin. In fact, given that you have effective drivers, provided by the board maker, and that there's still a source (Toshiba) of 82C55's, AND that you'll be operating slowly enough that any 8255, even the slowest, will work, I'd say it's a good idea, provided you don't get too attached to them. Using 8255's is pretty much like using on-chip I/O once you're set up.

" -- optionally wire-wrap a prototype."

a good idea if you can stick to CMOS hardware, i.e. no form of bipolar logic, at all, EVER! since you're battery-powered.

" -- get some PCBs made."

well, that's up to you. I'd concentrate on the packaging problems first, since that often is a bigger problem than PCB design. You'll probably want a WOODEN box, so it looks and feels like the "classic" chess clock. Putting the batteries in the bottom will put the weight in the right place. I'm not sure what you're doing with those rotary switches, so I don't know where you'll want to put 'em. What other features have not been mentioned yet?

" -- if all the world comes saying "sell me one of your wonderful chess clocks" then I might think about hiring a student to stuff a hundred more PCBs."

that would be nice.

RE