Yeah, after thinking about it, I think engaging the nipple on the tank directly is probably the best option. With a manual lever then you could 'burp' it like you say, and it would be trivial to add a cheap solenoid.
The automatic suppression system part was indeed more to save the house than the cutter -- something so that I don't wind up peeing in a jar during a long, complex run because I'm afraid that the moment I step away and go to the bathroom the cutter'll flare up and burn the house down. But I think that it'll be possible to build the system so that it engages before that point.
You're probably right that an IR/computer vision solution would probably be best, but that's a lot more complexity and another expense that I don't want to add.
I immediately discarded any particulate based method of fire detection, since just cutting some materials can generate a lot of smoke. I still think that a heat-sensor approach is the best compromise between reliability and simplicity.
Now, since I don't have any real hands-on experience with laser cutters, this would require some testing, but I have a feeling that the best place to measure air temps to determine whether or not something was on fire would be right in the center of the exhaust ring, with the vertical position being close to the level of the cutting platform. That should be the first place to reliably experience an extreme temperature rise, and in a skinned cabinet that's being exhausted through it, likely to be experiencing the most extreme temperature at any particular time outside of whatever's actually on fire. Again, I'll have to test this to verify, but I have a feeling that there'll be a good spot at around 175-250 degrees F -- hot enough that it's not a temperature that you'd run into at that part of the system during normal cutting and small, brief flares, but low enough that the rest of the machine won't have melted / caught fire yet. You could even calibrate it thus by burning progressively larger bits of paper on the bed of the cutter, with the gantry moved out of the way and any sensitive bits of the machine covered with aluminum foil -- or better yet, before you've installed the belts, lenses, mirrors, and electronics, but with some sort of skin in place with similarly-placed exhaust and intake holes, and the exhaust pulling. Once you've made a fire big enough that you'd want the system to engage, look at the exhaust temp, knock a handful of degrees C off of it, and that should do it.
As to small flare-ups during the cut, I imagine that it might actually be more useful to have a separate system that's routed through the air assist of the laser, or otherwise attached to the gantry. By not attaching anything to the tank, in the fire-suppression scenario, to extend the tank lifetime as noted above, it means that you basically have to flood the cabinet pretty well and blow a decent fraction of your CO2 to get an effect. Now, this is perfectly fine as a 'scram' option, it's very inefficient for the kind of more precise assist that you're talking about. On the other hand, a manually-actuated CO2 assist is just a matter of a CO2 tank, a T-connector into your air assist, some tubing, and a hand-actuated valve mounted to the tank -- you might be able to salvage one from one of those crappy portable gas grills that rot out if you sneeze on 'em, but I don't know if the threads and couplings match. I've also heard of people using old SCUBA tanks as CO2 storage/dispenser systems for paintball; that might be an option if you want more CO2 than you'll get out of a 20 oz tank but don't feel the need for a big welding tank.
In other, bad, news -- it looks like I'm not ordering my first batch of parts this month. Realized I needed to buy a suit for an upcoming wedding. There went my voluntary expenditures budget. Oh joy, that gives me more time to waffle between "just build it as directed so you don't run into any unanticipated problems" and "but I really want a bigger cutting bed!" (Yeah, I'm one of those annoying kinds of consumers, at least until right when I pull the trigger and commit on a big purchase, but I think at this point I'm leaning towards 'make it bigger.')