I'd go with the uninstall/install route instead of fighting with it. If the reboot is the issue, give your agent uninstall and agent install packages to your software distribution team. Do the uninstall/install routines when your Windows patch cycles come around. Install patches, uninstall the agent, install the agent, and then reboot as part of the normal process. Make sure you use the results of "UninstallPwdKeyGenerator.exe" for your uninstall password in your batch file, or transform.
Pg. 93 in the Windows DLP install guide,
"Passwords can only be added to DLP Agents during agent installation or upgrade.
If you have existing agents you want to protect, you must remove the agent and
then reinstall the agent with the password."
In the case you have described, you are not upgrading agents. You have existing agents. So, your ticket to an uninstall password is, unfortunately, uninstall and install.