I'm very late to this thread, but if you're still in question: Yes, the Stromberg "W" is a one-year-only item. It is a very well designed carburetor, with castings of substantially better quality and a more advanced venturi design than the Holley 1920 and Carter BBS carburetors that were more common on slant-6 engines of that timeframe. Also the Stromberg W has no gaskets below fuel level, which is nice for preventing fuel leaks and is not the case with the BBS or 1920.
The 1963 B & C body Dodges and Plymouths with 225 engine were the only applications for this carb. There were only ever two models: the WA3-219 and the WA3-219A, which had very slightly modified off-idle transition provisions. No other WA3 carb was ever made for any other application. It's difficult to imagine why Chrysler would have seen fit to pay the enormous costs for design, tool-up, and production of a carburetor for just one year; the only explanation I've been able to come up with is for some reason Carter and Holley couldn't supply enough carburetors to keep up with slant-6 production demand. The Bendix Stromberg carburetors, whether 1bbl or 2bbl, were more expensive than the Carters and Holleys, so I guess whatever situation caused the Carter/Holley shortage in '63 was alleviated in time for '64 production. One interesting note: this carb has the largest venturi diameter of any 1bbl carb factory-installed on a slant-6 engine. It's also interesting to note that Chrysler Australia used a similar (but not identical) carburetor made by the local Australian Bendix outfit on slant-6s in '67-'69.
Back to your W: the carb kit you need is indeed a tough item to find. None of the usual or unusual kit suppliers can provide it; it hasn't been in anyone's product line for many years. I have one kit left on my shelf (I'm not using it in the foreseeable future, so would be up for selling it; send me a PM if you want to buy it), and occasionally I see them go by on eBay. If you need the service info on the carb, I have that, too. I even have a few of these carburetors, complete. Before you do the rebuild, you'll want to carefully trace the one and only gasket (air horn to main body) and hang onto the tracing in case you need to make yourself another gasket someday and can't find a kit. All the other kit parts are easily available -- the accelerator pump plunger/cup assembly was also used on Stromberg WW 2bbl carbs, as was the inlet needle/seat, and check balls are not carb-specific.