After a while, I decided to flag these posts to alert the mods that this troll is back with a new account. While this is doing well for my progress to the Marshall badge, I can't help but feel that this adds pressure on the mods. Should I stop flagging these and let simple downvoting trigger Community (the automated diamond user) to delete the post/user? Or is flagging the right way to respond to this troll?
Please flag, absolutely. And... do nothing else at all.
That gives us the least work - often none at all - and gets rid of the troll with the most dispatch, and with the least satisfying interaction from their point of view.
Use the Spam flags, please; those have the most direct effect. And if you really want to, you can add one "Other" flag letting us know about the account itself. But, my guess is in most cases, we're going to kill the user a while before we ever see that 'Other' flag. I tend to check out accounts that get Spam/Offensive flags to see if there's anything obvious, for instance. (Since spammers/offensive folks tend to have habits...)
By all means, mods are there to handle your flags. Don't worry about putting pressure on moderators if all you're doing is flagging potentially abusive behavior. You're not gaming the system—you're flagging posts or users that need attention.
If moderators don't want to see your flags—for example because they are invalid and don't require action—they would simply decline them or let you know through a moderator message. And if there's a moderator who isn't sure about what to do with your flags, they'd just pass it on to another mod or the community team.
That being said, if you cast one flag per user account, that's probably enough. You wouldn't have to flag each post, for example. On higher traffic sites, casting offensive or spam flags would kill any post faster and without moderator intervention. On lower traffic sites where the flag queue isn't as big as on Stack Overflow, a custom flag would also be helpful.