Not to be a downer but before taking the plunge to making your TW off-road only (green sticker) I would recommend you find-out what the back fees will be on your bike. You can do this on the DMV's website, all you'll need is the license plate number and maybe the VIN number. There is really no way it can be in the thousands, there is a limit on how high the fees can be and if it hasn't been registered in the past 10 years your golden, it won't be in their system at all! No back-fee's or penalties. Going the green sticker route the DMV will still want to their back fee's. By the way these back fee's will NOT in any way effect your driving license; you can still renew your driving license if you have a non-registered or un-registered vehicle in your name.
Another argument against going green sticker (off-road use only) is it will kill your re-sale value since once it has been registered off-road only you can NEVER change it back to on-road, thus limiting your pool of potential buyers in the future. It will also limit by a large amount where you can ride. Green stickered vehicles can not ride on fire roads in the mountains or on the dirt roads in most (if not all) of the state parks in the state.
It sounds like you've gotten some bad information, if you would like PM me and I will be happy to help you navigate the mess which is the CA DMV. I have played this game many times and know at least most of the in's and out's of the system.
Kevin