I've long since taken all valuable data off the notebook and placed it on my external hard drive.
Well, backups might need to include not only documents, but settings too. For example, if you don't want to call your ISP for some configuration data (in some cases, not necessary, but it might). Other classic example are Outlook (or similar) emails, contacts and settings.
I'd have no hesitation in restoring factory settings as there is nothing for me to lose. I do not know how to perform this task, however.
Well, that depends on your specific notebook. Probably the support website of your specific notebook has this info.
JFYI, after Factory Defaults, you would need to (recursively) apply Windows Updates, re-validate your Windows installation and reboot, and then repeat the process until no new Validation is needed and no Updates arise.
After that, install Avast anew, scan with Avast your backup and solve any conflicts, and restore your backup documents.
Next time, when you have an infection, better to send to the chest instead of deleting all files. This action (chest) might not completely solve the problem, but at least it gives a clue about it.