I saw your post and thought I'd shoot you a message to try and answer your question about the Huey. I am a former FAA inspector, and I've been an FAA Designated Airworthiness Representative for the past 20 years. I specialize in the type of aircraft you asked about. I have also certificated quite a few Huey's.
The UH-1E is eligible for certification in the Restricted Category under the Type Certificate that Robert Mena mentioned. JR Helicopters does in fact hold that Type Certificate but remember that such a certification is for very specific and limited purposes... aerial application, search and rescue, forestry, etc. You would not be able to use it for pleasure flying if it was certificated in the Restricted Category.
Additionally, if the data plate has been removed and is no longer available, it will not be eligible for certification in the Restricted Category, period. In such a case, the only available route would be to certificate it in the Experimental-Exhibition Category. There are limitations on Exhibition aircraft but you would be able to fly it to airshows, hire it out for movies, use it for static displays, as well as maintaining proficiency. There is no limitation on proficiency flying.
The Forestry Service, a government entity, flew the aircraft as a Public Use aircraft, which did not require any type of airworthiness certification. Once it left government service, different rules apply.
The major problem, as I see it, is that there are no records for the components. Almost all of the rotating components are either life-limited or required to be overhauled on a required time basis. If you don't have the records, you have no way of determining how much time is left before a component needs to be retired, so that component must be discarded. If you start throwing away a lot of components, it becomes a VERY expensive proposition! In fact, many of the components for that model helicopter are not available anymore.
The bottom line is that such an endeavor requires a LOT of research, time and money.
If you are truly interested in a Huey, I would suggest calling Jim Ray. He currently has a UH-1K that is for sale with complete records. I do not have any financial interest is Jim's helicopters so I'm not pushing this one for any gain. I just know its history and know that it's ready to go.
You can feel free to contact Jim personally to ask him about his helicopter, and you may also call me if you have any questions about how such aircraft are certificated and flown.
Brian Ingraham - 713-410-1486