First, am I close with my understanding?
That is pretty much how it works. There are some minor variations on the theme. Nitrox regs that use this approach use an O2 compatible grease like Christolube which is a little runnier and a bit more water soluable than silicone. This, and concerns for cross contamination of silicone on the tools and workbench between nitrox and non nitrox regs was the reason SP stopped using the Silicone Protected Environmental Chamber(SPEC) system and went to the less than 100% effective Thermal Insuslating Sytem on their piston regs.
If so, is this a viable way to deal with the problem?
The SPEC system worked great - as long as the ambient chamber was properly packed and the right grease was used. The Silicone SP used was thicker than the silicone grease available from Trident. With the thinner silicone grease, you may need to repack it mid season. But when properly done, the first stage is very freeze resistant.
This "seal" surely isn't water tight? Won't the seal leak salt water in still, but this time will keep it in--as opposed to not having a seal?
The above response answers a lot of this, but yes, if you let the chamber get partially empty you end up with salt water in the chamber where it basically stays. Over the short term it is not a problem as the silicone will still be stuck to the metal parts and protect it from corrosion to some degree. It however becomes a problem in cases where the owner decides to skip an annual service.
And although the seal will keep most dirt out, it seems to me that the dirt that does make it in will be trapped?
Yes, it does get trapped and the silicone you remove at the next annual service will be quite dirty. The particles are however very small and do not seem to create any noteablel degree of wear (there is after all lot of lubricant in there) unless again the owner decides to skip an annual service or two.
Lastly, won't the goo leak out fairly rapidly, leaving a pocket of "sealed in saltwater?"
Hot weather and or leaving the reg out in the sun will warm the silcione grease and cause it to thin and leak out faster. Over time this can be a serious issue, so again topping it off mid season can be important.
Improper packing where voids result deep inside the ambient chamber and or between the spring and piston is a bigger issue as they compress with depth, allow water into the chamber and over time the water will migrate to the interior voids. So proper packing is key and not many Scubapro techs out there still know how to do it well as Scubapro has not supported SPEC systems in over a decade.
There are a couple piston designs around that use a sealed ambient chamber where air is bled into and retained in the chamber by various valves, but they are complex and tend to be problematic in service. Sherwood uses a bleed system on some of their models where the chamber is not sealed and where the excess air bubbles out in a slow stream. It has the virtue of simpicity, even it it will never pass a bubble check.
I agree with the suggestion above that if you really need a cold water reg, get a diaphragm reg that also has a diaphragm sealed ambient chamber. Not all diaphragm regs are fully sealed. The Scubapro Mk 17 is currently one of the best, and in my opinion the best cold water first stage available and it offers more than enough flow rate for any technical or recreational diving need.
If you decide to go the SPEC route, get a used Mk 20 with the later MK 25 piston and then add the late production MK 15/early production Mk 20 SPEC boot. It is a lot wider than the earlier narrow SPEC boot used on the Mk 10, Mk 10 Plus and early Mk 15. The extra width provides some room for expansion of the silicone and helps to both retain the silicone and keep the seawater out.