I also have an '84 QT50 (also called a Yamahopper). In fact, the pic of the red one with all the accessories and the ugly dude standing behind it is mine...
I've done lots to mine to try to get it to go faster... Drilled holes in the aircleaner, tried different sized jets, replaced the stock muffler with a VW tailpipe... The thing that made the most improvement was taking the cylinder off and cleaning the ports.
From what I understand, the CDI ignition limits the speed to 35 or so, so I'm not sure you can get it to go faster than that. I'd like to try playing with the timing, when I figure out an easy way to do it.
One of the mechanics at the local Yamaha shop told me that the drivetrain on the PW50 is indeed the same, and if you look at one closely, you'd probably agree. I don't know if parts are interchangeable, but it sure looks like it bolts up the same way.
If you need a manual for it, check Ebay. That's where I found mine, and I saw another one there recently.
The stock muffler has been discontinued and is no longer available thru Yamaha. You may have to buy a Biturbo for another brand and modify it for your QT. That's what I plan to do, when funds permit. Or, you may be able to use an exhaust from a PW50, but I'm pretty sure the frame mounts are different.
Where are you at? I'm in Greenville, SC... Let me know if I can be of any assistance...