Striping a machine is never going to be much fun, but if it's an area you think you could have reached with a Dremel, then I'm guessing it could be possible to get in there with a cloth and some fine cutting paste. It's tough work doing it this way, and you must make sure you get rid of all the residue, but you can get some good results, and it would save you going the whole hog. You should spray on some cleaning fluid first like Novus, then the cut, then more Novus, then simply wax it after.
Failing that, as has been said (although maybe got taken the wrong way accidentally), you would have to remove the bits to get to it properly. If you don't want an entire strip, then you could at least remove enough to make it easier for you to get to the localised spots you want to work on.
I don't know LLoyd, but it's my experience that most people on here are pretty helpful towards each other, but sometimes comments don't seem to be what you expect or seem to be a little short or blasé. People who love there pins sometimes forget that not everyone wants to wade in and strip a machine right off the bat, where as others wouldn't dream of anything but a complete strip the moment it comes through the door. Generally it's just one persons manor not fitting in with someone else's. But usually it's just it aimed in the right direction.
Good luck there chap and welcome to Pinside.