My apologies for not ending the discussion sooner... the carb kit arrived late in the day yesterday, and with the poor weather today I was able to replace the suspicious metering diaphragm and do a proper rebuild. After reinstalling the carb, with a bit of tuning, the saw now runs very nicely, starts up, revs up, runs, and idles well once warm (takes awhile at 10 degrees Fahrenheit). A bit of sharpening to the dull chain and it even cuts nicely.
Regardless of position, the saw holds idle, doesn't run erratically when laid on either side, and overall does what I expected it to.
Thanks again for everyone's sage advice and words of wisdom.