How bad is goo gone for cleaning melamine racks?

I recently bought a used rack that I have to completely redo the flexwatt. It had 3" flexwatt, but of the three inches, only 3/4" was exposed. It was covered by foil tape and no heat was going through it. I verified this with a Fluke 62 Mini IR Thermometer. The only heat was from the flexwatt that wasn't covered by the foil tape. Here is how much of the flexwatt was exposed.

http://i29.photobucket.com/albums/c2...ky27/photo.jpg

So after I peeled it off the melamine, there is still so much foil tape stuck to it. I worked on one shelf (of 10) for 45 minutes and I still don't have it all off. I tried Goo Gone, which isn't helping much at all. The smell is very strong and I'm worried if this will be bad for the animals once it is finally done. This is what I'm trying to get off the shelf:

http://i29.photobucket.com/albums/c2...sky27/-1-1.jpg

Should I keep going with the Goo Gone? Do you guys have any other ideas? I was thinking of using a razor blade, but I don't want to make any cuts where any moisture could get into the compressed wood.

Any help would be much appreciated!

Olive/vegetable/mineral oil are all pretty good at getting rid of adhesive, with the upside that there are no fumes or anything to harm the animals afterward. This is what I've been most successful with. I'd just use tons of it and a putty knife...and persistence.

WD-40 would also work the same way, but probably more likely to leave behind dangerous residue.

I've also used baking soda and water, and the baking soda is abrasive so it works but I don't know if it would damage the melamine.

Besides the above suggestions the only other one i would make is to just buy new flexwatt. The stuff is really cheap so if you dont wanna risk harming your bp with something like goo gone you could just buy some new heat tape. Just my .02

Goo gone is basically paint thinner and citrus oil. The thinner will evaporate after some time 48 hour or more but the oil... would need to be removed. WD40 is propellant and fish oils again it leaves a residue behind. I'd try olive oil myself and then an alcohol wipes after than. But to be completely honest I too would start fresh. After you remove all that tape and check connections ect it would likely be less time to start over.