@CDobyns,
This posting has been noteworthy in its one-sidedness (replies mostly from myself), but I thought I would add to it a little further, and probably effectively close it out.
Since I wasn't able to elicit a viable solution to clear what I think is a plugged carburetor, I decided to pursue just purchasing a replacement carburetor altogether. I opted to go through eReplacementparts (www.ereplacementparts.com) for a replacement carburetor, and that proved to be a fairly easy and cost-effective solution. The new carburetor, plus shipping, came to $29, and needless to say, purchasing a brand new blower would have cost somewhat more than that.
Replacing the new carburetor involved removing three screws and reconnecting the fuel lines - and took about ten minutes, and the blower fired up on the very first try at starting it. With that success under my belt, I decided to replace the carburetor on a string trimmer, which had a similar problem and had not worked in more than seven years, and that replacement was also successful. So, my recommendation is that if you have this type of problem, where a gasoline fueled device won't seem to start - summon your courage and your wallet and just take the (small) risk and try swapping out the carburetor. That's probably going to solve the problem and is a relatively easy fix.