Probably the best procedure for dubbing these tapes would be to only play them soon after baking and cooling.
Assuming that the "treatment" that the seller mentioned was baking, it's only a temporary fix. Depending on the original condition of the tape (how hydrolyzed), the baking, and the humidity that the tape's been exposed to, the "fix" might last for months, weeks or days.
The biggest problem that these sticky tapes have is when the back coating and the oxide stick to each other. When this happens, either of these coatings can shear off of the backing effectively ruining that section of tape. Once either of these coatings pulls loose, there's no repairing it. Because of this, avoid playing these tapes when sticky.
So, wait till you have your dubbing system totally set. Bake the tapes and dub them within a day or two. Rest assured that no matter how dry an environment you store those tapes in, hydrolysis begins as soon as the tape cools.
Even if you are able to play through the tape without it stopping the machine, squealing audibly or slowing the tape speed, if the tape is depositing on your tape path, the sound will be effected. The main culprit here is the "stick-slip" of the tape movement (scrape flutter). Deposits on the heads will also cause level imbalance caused by spacing losses.
Your lucky, not only is an A80 a fantastic machine, it's tape path is one of the best for minimizing issues with problem tapes.