...if there is a signed document which the church has in its possession..it is not available to be seen.
The only value of having a signed document is to display it as evidence/proof to others of the statements made in it. Since 1830, the LDS Church has published a printed version of the testimonials, as part of the Book of Mormon. In my experience, the only time a signed document is held back, when its contents are known, is when the signed document does not exist. Indeed, the intros read, "Be it known unto all nations, kindreds, tongues, and people, unto whom this work shall come: That... ." Odd that they'd only want it known through typeset, not with the ink of their quills in signature on the original.
I'm also under the impression that none of the witnesses talked about seeing the plates other than with spiritual eyes or the supernatural. If that were the case they wouldn't want to sign they had seen them.
"...we, through the grace of God the Father, and our Lord Jesus Christ, have seen the plates..." Given Mormon speak, it is a good point that the testimonial did not specify whether it was physical vision or only 'spiritual' vision involved. The artists' renderings of these events do not give the plates an ethereal, angel-like lighting around the plates, suggesting that it was physical plates, with physical eyes. The LDS Church promotes these portrayals by including them in their teaching materials.
"And we also know that they have been translated by the gift and power of God, for his voice hath declared it unto us; ... ." Is this a physical voice, with sound waves, or in the mind's ear? or perhaps a bosom burning?
"And we also testify that we have seen the engravings which are upon the plates; and they have been shown unto us by the power of God, and not of man." Very suggestive of supernatural, no physicality to the event. Otherwise, what is meant by 'the power of God, and not man'?
"... an angel of God came down from heaven, and he brought and laid before our eyes, that we beheld and saw the plates, and the engravings thereon; " Physical or spiritual?
"and we know that it is by the grace of God the Father, and our Lord Jesus Christ, that we beheld..." Is this hearsay via the angel? via JSJr? Is this assumed because it had a supernatural element to it? Or, did god and Jesus appear to these three witnesses?
"the voice of the Lord commanded us that we should bear record of it; ... ." So how do they know it was the Lord's voice?
"we bear testimony of these things." But if anyone has the original bearing signatures by these witnesses, it needs to be kept hidden?
As for the testimonial of the 8, "Joseph Smith, Jun., the translator of this work, has shown unto us the plates of which hath been spoken, which have the appearance of gold; ... ." More substantial evidence, in my opinion, than the testimonial of the 3 (assuming both could be authenticated and proven genuine). Here, unlike with the 3, the 8 are saying that it was JSJr, known to be a real person, showed them the plates. This does not open itself up as widely to the shake and bake apologetic that it was with 'spiritual eyes'.
"we did handle with our hands;" Never heard any mortal having claimed to touch something with his or her spiritual hands in the way we sometimes hear about 'spiritual eyes'.
"and we also saw the engravings thereon, all of which has the appearance of ancient work, and of curious workmanship." Ancient work? Could that mean that the plates the 8 saw appeared less skillfully prepared than the technology of 1830 could produce?
"for we have seen and hefted, and know of a surety that the said Smith has got the plates of which we have spoken." Haven't heard of 'spiritual hefting' either.
But whether they signed or not...is not particularly important. The statement from both sets of witnesses is problematic for a number of reasons..in particular imo that the statements make testimony to things they could not possibly have known.
I agree there are a number of problems. But just because there is no possible way that the 3 or 8 could possibly have known some of the things in their statements (lack of foundation), it does not follow that other claims in their statements, claims that they could possibly have known, are necessarily untrue or without foundation too. So, I think that it is particularly important whether those 3 or 8 ever signed a document to the effect purported in the publications of the Book of Mormon.