I am not so sure I would spend any money fixing your plane up until you get your paperwork problems under control. You may simply may not be able to solve those problems satisfactorily, at which point you will have a pile of worthless junk that looks like an airplane.
If the original kit manufacturer is around or a successor company, you may be able to track down the original buyer, who can then help you with your chain of ownership problem. If the company is now out of business the FAA may accept a letter from you stating that, in lieu of an original bill of sale, but you would still probably need to get something from someone who is willing to say they bought the kit from the manufacturer. If you can't get any of that I suggest you call the EAA and ask them if there is anything they can do to help. (You should probably do that anyway)
Besides your chain of ownership problem, if the plane is fully assembled and there is no evidence to support the claim that it is amateur built, you have another problem. To secure an experimental amateur built airworthiness certificate you need to be able to convince a DAR that it was indeed built by amateurs for their education and recreation. This is typically proved with construction photos and a log. Without any of this you have a serious problem to which there may be no good solution. You might be able to get it approved for some other experimental category, but without amateur built status you have something of little practical value.
It is imperative that you connect up with the original builder if at all possible. You may also want to consult with a DAR in your area who can take a look at your situation and tell you exactly what you are going to need to get an airworthiness certificate. Your local EAA chapter is a good place to ask about a DAR, or your local FSDO will have some names for you. I suggest you do that before you spend any more money fixing the plane.
Good luck with all of this. It sounds like you are going to need it.