So I got the following response from Webroot:
"The issue you are reporting is most likely a known issue related to the Identity Shield protection layer. The Webroot Development team has been notified of this issue and is currently working on a resolution. We expect to address this issue in an upcoming software version release, which will be downloaded automatically to your computer and installed when it is available
In the meantime may you please try allowing Task Manager (taskmgr.exe) and Chrome and/or Firefox (chrome.exe and/or firefox.exe) on Identity Shield by sending an 'Identity Shield Allow application' agent command following the instructions below
[...]
Finally, please reboot the machine for it to take effect."
Previously I had allowed both Firefox and Task Manager in Webroot, but it didn't work. They essentially suggested the steps I had already taken, with the caveat that I should reboot my machine for them to take effect. In my case, at least, a reboot following these changes has worked and I can now access my Task Manager as normal with no lag, even with Firefox open and full Webroot protection enabled (with the new exceptions of course)
I'll monitor over time and report back any changes