I really don't want to have to sweep my entire system and reinstall all of my applications and reset all of my settings, etc. if I don't have to.
You might have to. It depends on exactly what you used MacKeeper to do.
Upgrading to Mavericks doesn't change any software that you installed, including software that modifies the operating system. Some software known to be incompatible will be isolated to a folder labeled "incompatible software" but the algorithm responsible for performing that action is very superficial and leaves a lot of notorious garbage untouched.
When an OS upgrade results in system crashes, slowdowns, and other unacceptable behavior, ill-conceived third party software that modifies OS X (such as MacKeeper) is the usual reason. MacKeeper isn't the only example. In general, you should uninstall anything of a "system utility" or "maintenance" nature such as "optimizers", "boosters", "cleaners", "sweepers", "protectors" and so forth, things that modify the Finder or the Dock - generally anything that isn't related to the tasks you need your Mac to perform for you. Uninstall anything that fits that description first, and don't reinstall it.
As a rule you should back up your system routinely, but especially prior to upgrading OS X. It's the only practicable way to "undo" an OS X upgrade, should you want to do that. Read: Mac Basics: Time Machine backs up your Mac
If you are uncertain if any well-known problematic software exists on your Mac, consider posting the results of EtreCheck. Read about it here. It contains a link to download EtreCheck. Don't download it from anywhere else (such as may be found by following the results of an Internet search).