The closest you'll get with that movement is a use or NOS Ebel Type E or 1911 Senior, both of which were made in the late 90's and early 2000's. Look for a reference number that started with 9080... (Ebel's caliber 080 is a Lemania 8810 and the 9 means the watch is steel). The sales tax on that one will be less than $100, but not by that much.
The Lemania 8810 was originally the Longines 990, which I think may still be the thinnest automatic with central seconds and date ever made. It's the only automatic movement in watches that are even remotely affordable that is thinner than 3mm.
Many automatics used in the 60's were not as thin but the watches in which they were use were very thin compared to current watches.
The closest you'll get is an ETA 2892 or Sellita SW300 (or Chinese clone, including the Seagull ST18), which are 3.6mm thick. Finding watches with basically finished ETA or Sellita movements in the several hundred range (used or very deeply discounted) is not impossible, and Seagulls with the ST18 movement (such as their 8mm ultrathin M201s) are in that same price range new. I think that's about as good as it gets for an ultrathin auto.
Now, if you can live with a handwind, there are zillions of vintage handwinds that would be called "ultrathin" today, being 7mm or so in thickness for the overall watch. One inexpensive option is a Favre-Leuba with their caliber 253, which is not hard to find for under a C-note but is hard to find without having a garishly repainted dial or a movement full of corrosion resulting from decades of Mumbai humidity. But there are many others.
Rick "thinking this is a tall order" Denney