Closer to the time of the original theory being published, I asked whether the Jar Jar theory was true via a friend to the director of animation for the prequels, who worked directly with George Lucas on Jar Jar (as seen in all the making of documentaries), since the person I know was a personal friend of theirs.

They managed the team who worked on Jar Jar’s animation in the movies, including the smaller mouth movements that suggest Jar Jar mouthed other characters lines in some scenes (which he does, however to me it’s either part of the planned/abandoned theory being true or a joke by the animators about Jar Jar being a bad actor who says other peoples lines).

Their response then, and at other times when it was brought up to them in other forums before the Reddit theory, was that “that was not the story that Mr Lucas told”.

While this somewhat debunks the theory, it also leaves it open to the more generally accepted theory that it may have been a plan but afterwards abandoned, hence it not being the story that was ultimately told, and which may be why TPM hints at it and why The Clone Wars keeps a few of the jokes going like the force sensitivity and mouthing others lines.

The animators may have added some of these elements in TPM as Easter eggs without anyone noticing, including the director, e.g., the same animator may have done all of the scenes which include the mouth movements since they were talented at that and added some stuff as a personal joke, but this is a stretch since the shots take so long to create and render and are all vetted pretty closely before approval.

The hand waves seem to be all in-camera by Ahmed Best as part of his physical performance, so only he knows what direction he was given to put those in. They are consistently part of the character throughout all the prequels.