Do you mean setting the time of day on the clock?

I was of the impression that one sets a maximal amount of time on the clock and it decrements one or the other player's remaining time, and complains if/when that time expires.

That, actually, would require four digits for each player, though it could be shared by means of a "set" button for each player, or some such arrangement.

Back when I activelyplayed competitive chess, which was decades ago, our clocks were set like an alarm clock, i.e. by means of a knob on the back of the clock. These ran backward, however. There was a reset button, one which, with some effort, set the clock to 00:00 (midnight) and you could set the thing to whatever time you desired, e.g. the 45 minutes during which each player had to make his first 30 moves. Since they were mechanical clocks, it was possible to introduce considerable error into their working, aside from the inherent mechanical variations.

I think you're right in focusing on simply building your own clock for your own use. From that you'll learn whether there is, in fact, a market niche for a clock with the features you envision. Further, you may decide on some additional features that you like. OTOH, you may find some things you don't believe you need.

I've never seen a digital chess clock, so I've got no idea at all what your settings might contribute, though I don't doubt that there's use for them.

Over the past half-hour or so, I've taken a look at the signals available on a 40-pin part and concluded that, if you use one signal FROM the "main" MCU (MicroControlUnit) which, based on what I proposed earlier, would be the one which reads the switches and does the timing, TO the two whose job it is to drive the LCD's, you can do the whole job with three 40-pin CMOS 805x types. The display-driver MCU's use 29 of the 30 available pins to drive the segments, and one to drive the backplane. Each receives an interrupt from the main MCU each time it has to increment its display. Where the oscillator to the display drivers comes from is TBD.

The "MAIN" MCU reads your switches, including the pushbuttons, and maintains the system timing. The actual time is maintained by the display drivers, since it's just a mod-60 count and a mod 12/24 count. BTW, if you're going to allow time in excess of an hour, you'll need more than 4 digits to display HH:MM:SS, though I'd not display seconds until the time is under an hour.

I've not had to buy an 805x MCU since 1981, so I've no idea at all what the majority of them cost. If you pick one that will go to sleep while leaving the timers running, then you can use that feature to great advantage, running your main processor for a few milliseconds out of each second. I'd use that feature for the display drivers, too. You'll probably find that it's more convenient from the standpoint of developing your prototype, that you use as little discrete SSI/MSI logic as possible, and, if you have to do so, add yet another MCU. If cost gets to be a problem, there are other options than the 805x, that come in high-pin-count packages costing only $2-3 on eBay, so it's likely you can solve your problem one way or another by using what eBay offers, provided you're careful. Many of the things offered there are OTP (one-time-programmable) versions of whatever they are. Those won't help you much. Some of the prices of the flash-based MCU's are quite ridiculously priced. OTOH, DigiKey provides a costly but relatively painless way of getting what you need. You can, of course, ask for samples, and, most of the time, will find they're readily available. Don't be too shy to ask, but don't ask a distributor. Call or email the manufacturer or his sales representative, and tell him what you're doing, without too much detail. You don't have to spin him any yarns. Just tell him/her what you are going to do with the samples you request. They know what a pain in the *ss it is to buy small lots. They know that any application into which their part is designed is more likely to yield eventual production quantity sales than one into which it's not. They also know that most samples sit on the shelf and are never used, so if they're convinced you'll do something with 'em, they're happy.

If you have any trouble getting parts, contact me directly and I'll see whether I can help.

RE