I've read your registration problem in your other posts. If you have the patience, I believe the issue will be resolved in your favor. Clearly, this was an error, humor or computer, that should be straightened out unless some past owner did something to make it an off-road only. If a conversion like this was done, it also makes common sense that it could be reversed as well.
If the DMV lady does not get a satisfactory answer from Olympia for you, I would start raising Holy Hell with the state and DMV. Someone, at some point in the DMV is being lazy, and has to use some common sense, look at the TW/ Dealer/Manufacturer information, and conclude a mistake was/is being made on the title...at the state level. I'm not even from your state and this DMV situation is making me made!
Go back to the DMV. Take all your paperwork and a writing tablet. Present your paperwork and state your desire. If you are told "No", politely ask, "What do I need to do to straighten out this error?" If the desk worker can provide no satisfaction, ask to speak to a supervisor. Write down whatever b.s. the official unelected goodermint flunkies tell you is the reason. Also, write down their names.
When you start asking for names and writing things down the local goobers are probably going to start getting nervous. Remember that they are probably poorly trained, over-paid unionized government workers whose retirement pension is completely funded by your state's deficit. They are really liitle more than trained monkeys and could easily be replaced by a form to fill out on an intenet web page. They are VERY insecure, but treat them nicely, anyway. Do everything possible to avoid a confrontational situation. I've found that "I'm sure something was messed up about this registration long before I brought the problem to you. Thanks for being so hopeful (it's just a little lie). I'm going to go home see if I can go on the internet and find out what we can do about this."
Then contact your stste-level elected representatives. An email will do--keep a copy in your sent messages folder. The email should include what you provided (which should be everything on the state website listing required stuff), what you desire, a link to the Yamaha TW200 page as evidence of the bike's appropriateness for highway use, the reason(s) the goobers gave for refusing to provide satisfaction, what you need to do to resolve the situation, and thanks in advance for helping resolve the situation.