Answering my own question here...
I found K-9 Mail Alpha, an email client app which DOES alow a different notification for each email account configured
I simply installed this app, added my accounts, and removed them from the stock mail app. Now I have different sounds for each account.
Here's the thing, though...
I have my default Gmail account for the phone, which uses the Gmail app. Nice app which allows setting a sound for the notification...but only works with the ONE Gmail account.
My work email is Exchange, so I configured it using the stock mail app. This app supports multiple accounts, but only the basic notification sound for all configured accounts. So I only have this app checking for my work email.
Then I have K-9 for the rest of my accounts since this app supports multiple accounts and multiple notifications.
That's THREE SEPARATE email clients...almost one for each account! I mean, that's fine with me for now since it's doing what I want...but seems like a bit of overkill.
I'll see if K-9 does Exchange, then I can go back to 2 email apps.
See, this is why I like Android...lots of choices and flexibility...a tinkerer's delight!
UPDATE: K-9 does Exchange! So now I have all my accounts (minus my main Gmail) in one email app! I still need to keep the old app setup with my Exchange info just to sync my work calendar, but I simply unchecked syncing of email. Now I just wish K-9 had a slightly better look
UPDATE #2: So...no go. K-9's support of Exchange is fairly weak and unreliable at the moment. Back to 3 clients.
UPDATE #3: Just wanted to say that I now use Touchdown Exchange, a very robust Exchange client, to sync my work email/calendar/tasks. I still have 3 email clients, but it's working great for me since I only open an email when I get a notification that I have an email, and I do it from the notification itself, so I never have to launch a specific client to check for mail. So the steps would be the same...get a notification, click on it to read new message, close it when done. Check next notification, etc.