Okay, I'm finally able to provide a solid update.
For my project, I've settled on using a secondary MCU to handle the functionality I was after. I am fairly confident this will be the solution I will use in the end. By way of explanation:
Using a MCU to provide a clock on its own is overkill and is one of the weakest solutions for the clock problem on its own. However, if the MCU can also provide other functionality, perhaps replacing or simplifiying enough other circuitry, then the effective cost of the MCU can be reduced to the point where it is competitive. My aim was to eliminate this as an option early on, but it ended up being useful enough that is became the strongest solution.
Having worked with AVRs in the past, I looked at the ATtiny series. Cost-wise, they are fairly good for MCUs, but unfavourable when compared to most of the clock solutions in this thread. There are a number of problems with existing solutions in my project that a MCU could potentially improve: Battery monitoring, low-power mode, and power management. Battery monitoring is the easy one: Use ADC and act accordingly. Running the MCU at battery/input power directly makes power management simple. As for low power, I was able to get battery use way down by simply using the MCU to switch off the voltage regulators that go to the rest of the circuit, and then drop to the lowest power mode for the MCU. Getting battery use down to 1uA (of which 800nA was power flowing backward through a diode and out via a pulldown) was probably the tipping point for me.
In the end, there is no clock signal sent out to the CPLD. Instead, the CPLD indicates when the emergency reset is activated (ie. four buttons down), and the MCU decides when it has been held long enough. I actually changed this in the end to treat the four-button long-press sequence as an escape that puts you into a mode in which you can select an option, one of which is an emergency reset.
As mentioned previously, I ended up purchasing a number of components that were raised in the thread to experiment with, and can share my experiences with these.
Due to my unusual start into electronics (I went straight to AVRs) I've never had a chance to play with a 555. I took the opportunity to rectify this deficiency and had a bit of a play around with one. I made a 50% duty cycle oscillator both slow enough to drive a LED blinker, and then one too fast to see. I finally got some use out of my multimeter's frequency measurement mode with this last one.
I next had an experiment with a 4060. I fed in the output from the 555 and hooked numerous outputs to my LED board, and admit to just admiring the result for a while. How odd that it doesn't have a Q11 output though. I hadn't realised/understood that you could supply two resistors and a cap directly to generate the input signal. Once I realised this, I hooked that up too and it worked great. Whilst I haven't tried two 4060s in tandem, I can imagine how it'd work. I think this would be an excellent solution if you needed multiple power-of-two clocks in a design. It's not expensive either- no wonder this was a popular solution.
I picked up, but haven't hooked up a MC1451B. I imagine the results would be similar to the 4060. The tradeoffs would be: Slighly smaller IC, can dynamically change the clock rate, can divide the clock further, but there is one clock out rather than ten, and it is more expensive.
I now have some standalone single-gate Schmitt triggers. I have reimplemented the delayed direct reset circuit I'd outlined previously using one of these. I haven't tied it all together to the CPLD, but adding in the Schmitt trigger should in theory eliminate the issues I was facing. Driving a MOSFET with a slowly discharging capacitor was never really a good idea. Having had a lot more time to search around for prices, it appears that this is one of the cheapest reliable solutions available (at the cost of accuracy). I think if the MCU solution falls over, this is probably the solution that fits in best with my project. It's also nice to have some standalone Schmitt triggers now- I didn't have any before.
I reimplemented the Schmitt trigger oscillator using a single gate Schmitt trigger rather than use the CPLD and a Schmitt trigger input. I haven't tied it all together to the CPLD, but the output of the circuit is digital, and in theory if I kept the relevant components out of the way of everything else I would be unlikely to run into the same problems I ran into previously, especially while breadboarding. I think that this is probably the strongest solution to the question originally posed at the start of the thread (cheap inexpensive low-accuracy 1Hz clock generator).
This thread has become an absolute treasure trove of information on oscillators and I really appreciate all of the input based on my initial simple question. I've learnt a lot, and I'm sure that others reading the thread have too. I have a collection of fallback solutions if the MCU idea doesn't work in the end. And most importantly, thanks to this thread, if I do need a standalone clock in the final design, or any other design I work on in the future, I have multiple viable options to choose from.
Thankyou all.