Someone over at MBAM suggested I restore these and scan again. I didn't want to chance it, but Avast found these things again when they were out of the Chest and I put 'em back. Had them there for about a month. There's also a "IPLogger.txt" on the desktop. I'm not sure what that is or how it got there. What do I do with these things now?
First and foremost what files are they suggesting you restore ?
If you have at any time uploaded these files to virustotal (as you have with rz11.tmp 15/36 detections) and had multiple detections then to my mind that is confirmation enough and a waste of time, no need extract (see below) to scan with MBMA.
Restoration to the original location is 'never' a good idea as it could reactivate malware.
Fortunately avast caters for this with the extract (copy) option where you can place it in a temporary folder like the suspect folder I had you create before and exclude so avast wouldn't alert in that folder.