I managed to fix the issue I was having with SSL filtering. Though, I decided to keep the feature disabled anyway due to the general security concerns with SSL inspection.
Even while the SSL filter was disabled, the Eset SSL Filter CA was still added to the Windows TRCA store. Removing it myself via certmgr.msc (while having the feature SSL filter disabled) allowed Eset to properly add or remove the CA. It now gets removed when the filter is disabled, and re-added any time the filter is toggled back on. And the filter works properly while enabled.
I believe this likely happened as part of the update to Windows 10 1151/Threshold 2, because the update process involves automatically removing and reinstalling Eset while retaining settings. I had removed Eset prior to my 7-to-10 upgrade, but wasn't aware that the 1151/TH2 update behaved the same way until after I had installed it. Microsoft's removal process seems to not fully remove Eset, causing the CA to break, while also preventing Eset from replacing/removing it. The PC was stuck with the 'old' Eset CA from the previous install.