So, I've made some progress. Avastclear was able to get me to boot into normal mode ONCE, but then subsequent reboots would display the same non-booting behavior.
I restored again and re-did Avastclear, but this time took a look around in that one boot to see what might be going on. I noticed that Windows Defender was having trouble starting, and the security section of the settings had a lot of [null] and menus that said that they were not working. Additionally, all the Defender settings were greyed out and unable to be selected.
Seeing this, I ran the DISM and SFC repair commands in Powershell, and afterward rebooted. This time, even without Avast, Windows was able to boot correctly and Defender (and its menus) were again working properly. To test this, I then re-installed Avast and then un-installed it after a reboot. Windows remained working.
I plan to stick with Avast as my antivirus provider, I was just wanting to figure out what the heck was going on with my computer. I don't know if this is going to work for good, but for the time being it appears to be working.