It sounds like you've got a real mess there.
Can I suggest WD40? Don't buy it in an aerosol can but in a 5 litre bottle (see: https://cpc.farnell.com/wd40/44506/wd40-5l-applicator/dp/SAWD405L).
It is good at removing old oil, gunge and grease from all sorts of things. I would not expect it to damage the tape but don't know for sure. After washing with it and thoroughly wiping there is usually only a very small residue remaining.