Amazing Thrills! in 3-Dimension was a Man... or Astro-man? promo 7" EP. It was released on Estrus Records (as ESP7) in 1993. The cover was printed in black and white on a thin paper sleeve that was machine folded and glued together. It only featured art work on the front side. It was only available on translucent black vinyl.
The count on this one is a bit tricky. According to the Estrus website, 200 copies were given away with their debut album, Is It ... Man or Astroman?, when it was ordered directly from the record label. 200 additional copies were given to the band for distribution--putting the total count of the pressing at 400. Here's a cobbled together screencap, in case the link stops working:
The sheet above was sent to record stores in the US and Europe to drum up sales for the first LP. The idea was that stores could order a bunch of the promo singles to sell at record release parties for the full-length. The sheet puts the retail sales numbers at 400 and the total pressing at 800. Since this was a document that predated the manufacture of the promo single, it would have been possible for Estrus to go with a larger or smaller number, depending on what the actual pre-order totals ended up being. Whatever the case, this one is devilishly difficult to track down.
Side A featured “Out Of Limits” and “Radio Promo.” Side B featured “MST 3000 Love Theme” and “Reverb 1000 (Live).” This is the first time Man or Astro-man's cover of the Mystery Science Theater 3000 theme song was released. It was later re-released on Destroy All Astromen!.
Here is a scan of the vinyl record:
The picture sleeve cover was designed by Stuart Ellis (A.K.A. "The Lounge Lizard"). Inspiration for the cover art looks to be taken from the 1953 sci-fi film It Came From Outer Space. The film was based on a Ray Bradbury story that told of a bizarre and very advanced race of one-eyed, amorphous creatures who could assume the form of any human in order to facilitate the uninterrupted repair of their ship. The aliens were not here to seize the planet or to enslave the human race, nor to destroy earth in order to be the ultimate life form in the universe. They just wanted to fix their space ship and leave--not unlike the "actual" Man or Astro-Man? origin story. Here is an image of the movie poster:
As you can see the four people and the mysterious eye are both taken from the poster. The EP's title is also pulled from here, as is the hybrid road/space ship condensation trail. The film was directed by Jack Arnold and starred Richard Carlson. The pair would also collaborate on 1954's The Creature from the Black Lagoon.
Thanks to Benjamin Brinkman for pointing me to the art source, and to Mike Noon for sending in a scan of the Estrus sell sheet.