I used a little bit of goop and a lot of friction with my gloved hands. It worked without damaging the paint but next time I plan on using a 3M eraser wheel.
Been doing the same on my door molding that I took off, am going to repaint with some Satin Black Krylon Fusion, and use 3M double sided tape to reapply. Bottom line. Just have to work at it. They came off the Jeep easy enough. If they are stuck on better then mine the dental floss or fishing line works. Just be careful because if you pull at the wrong angle you will dig in and cut the molding. I removed the excess off the Jeep with those plastic razor blades.
As far as getting the residue off the Jeep itself an eraser wheel kinda worked but you have to be careful to not burn the paint. I also tried the Duplicolor Grease and Wax remover but that required a little elbow grease and I did haze my paint a bit. I ended up using WD-40 and soaking it and just working at it with my fingertips and the plastic razor blades. Not fun. As far as getting the double sided tape off the molding. Very carefully used a real razor blade to get the excess off. Picked at it a bit with the plastic ones. Eraser wheel worked but left eraser wheel residue on the molding. That could kind of be cleaned up with the Duplicolor stuff. But still have bits of residue on the molding. Right now using rubbing alcohol and the rough side of a dishwashing sponge to get off the last bit of the residue.
All in all not fun. As far as the repainting of the molding goes am going to scuff them up a bit, clean with the Duplicolor stuff, use some Duplicolor Adhesion Promoter, and paint with the Krylon mentioned above. Right or wrong that is how it is going to happen. If I had to do it over again think just use the plastic razor blades on the doors with the WD-40. The molding would be both the real and plastic razor blades with the alcohol and dishwashing sponge. As far as the painting goes have not done that yet so after I screw that up might come up with a better plan learning from my mistakes.
There is a poly wheel that mounts to a drill that is used by body shops. It will peel up pin striping tape and the adhesive you are talking about without messing up the paint. I actually made my own by mixing up some poly and making a round puck, then mounting a shaft through it so I could chuck it in my drill.
I used Goof Off and plenty of elbow grease. I sat on a bucket with my ear buds in on a Saturday morning for a couple hours. Didn't seem to hurt my paint, but I really don't care much as long as I don't get rust. The sides are scratched up from branches (etc) anyway.
Edit: oh ya! WEAR RUBBER GLOVES!!!! My fingers were torn up for a good week.
I use the best power washer I can find. It'll actually blast most of it off. Then some kind of goof of type stuff, 3m used to have a good adhesive remover, and a plastic razor blade.