@KFrank
Great points re the ability to interpret “None” as “recovered at home”!  Now that you mention it, I KNOW there are examples in my dataset in which Pneumonia was indicated AND the patient still recovered at home!
As for confounding factors related to cases that have not yet “concluded”, I controlled for those by only considering cases where the onset of symptoms was more than a month in the past.  That has it’s own set of issues (e.g. it won’t reflect improvements in treatment in real time), but at least 99+% of cases will be resolved one way or the other by then.
I think my path forward will be to add in the 5th “HomeRecovery” label without excluding pneumonia cases.  I’d also love to be able to capture the “Never Sick” vs. “got sick but still recovered at home” distinction, but it’s just not present in the data as far as I can figure.
Finally, to your last point, I realize I’m out on a limb here by trying to interpret my outputs as probabilities, but…  That’s exactly what I’d like to be able to do.  Hence my struggles interpreting accuracy, I guess…  
Regardless, I really appreciate your insights!!!  Thanks a ton!
–SEH
EDIT: Changed “solution” to be your first response rather than my initial reaction to mark the second.  The first response will likely be more valuable to users with a more typical use case.