What would you expect when (if you are getting the same location as the OP) scanning the virus signature files is likely to produce the same issue.
It is essentially still a conflict, avast also has low level drivers to be able to actively inspect files, etc. these actions could well be considered suspect.
So it isn't just running two resident scanners, but when scanning Avast files and locations could result in a false positive. So you have to look at the location and file and ensure it isn't Avast Antivirus related.
Why the hell would you want to delete Avast files (and screw with your avast installation) if they are essentially false positives.
Ok, but that still doesn't explain why these EEK results are happening
now. Like I said, I've used EEK as a supplemental tool for two years now, with Avast Free on my computer that whole time, and this is the first time I have produced these scan results. There's also the fact that it isn't identifying every .dll file in the Avast folder, just that one (aswJsFlt.dll) in particular. So, maybe there's an issue with that particular file? Maybe it would be replaced in an update? I also did a clean install of Avast two days ago for unrelated reasons, so perhaps something went wrong in the installation process, etc. There are plenty of reasons why it would show up on a different virus scan aside from "don't have two AV software installed."
I don't trust Emsisoft since I've used their Emergency Kit scanner in the past, and it's not very reliable in detecting malware, PUP or any other type of virus side by side with Avast.
I strongly prefer MalwareBytes (MBAM) side by side with Avast, MalwareBytes has been very reliable for years in detecting malware, PUP or any other type of virus side by side with Avast.
I have used MalwareBytes in the past (like early 2010s) and liked it, but over the last few years a full C drive scan took anywhere between 16-20 hours to complete, so I stopped using it for that reason.