I have to try that hair dryer trick on my A500 box. It didn't have any tape on it when I got it -- then we moved and paid the movers to pack the household... I was at work while that was happening and some moron taped all over my A500 box with brown packing tape -- he must have used half the role.
My own tip: I can offer the tip for removing grease/oil from the cardboard packaging.
A few years ago I noticed in the street close to the place where I worked a small skip filled with building rubble. And sitting on top of that -- a cardboard sleeve for C64 breadbin! Unfortunately, it was all drenched in motor oil; the poor thing was really heavy and smelly. Someone must have been using it on the garage floor. I wasn't sure if there is any way to rescue this but I decided to try as I had the Styrofoam insert but not the sleeve.
A bit of searching revealed a trick for removing grease stains from wallpapers -- buy some cornstarch, make a thick paste, cover the stain, leave it dry, scrape it all off then repeat if stain still present. About a week and 1 kg of cornstarch later, the sleeve was not greasy to the touch any more (although the inside still looks like grease paper) and the smell was mostly gone. Eventually that small disappeared completely even though I haven't managed to extract all oil so I have to be carefully not to put that box in direct contact with any other cardboard box as it will stain it over time.