I wouldn’t recommend the wick method for this job unless you want to spend half a day just removing solder. Also you risk lifting pads and traces when applying that much heat for that long. You need to get in and get out quickly before desperation and frustration set in, leading to aggressive use of heat and force.
In another thread it was suggested to buy a Hakko FR-301 Portable Desoldering Tool which I did but have not done the job yet myself. I was hoping someone could explain how to check for DC offset on the transformers “while we’re in there”. I suspect this is why people are getting varying satisfaction out of the mod.