Thanks Mike,
Let it be known that I am a serious researcher. My analysis of the Geha, Remo, etc. is objective, aims to find verifiable facts, and was never along the lines of "oh, let's revise history and make these things into K-guns."
That said, I will get on to answering some legitimate questions posed by ClapperZapper...
"My understanding of these conversions is that they stem from the Treaty of Versailles?"
Kind of. Not directly, but more from the paranoia in Germany at the time about "our army is gone, what next?" The original D.R.P (Deutches Reichspatent) was issued in late 1919 for Gebrueder Rempt, better known as Remo-Gewehrfabrik. Remo also made some absolutely splendid rifles that go in the $10,000-$15,000 range (check out some of their boxlock stalking rifles if you get the chance...they also made double shotguns, but I've not seen any except in catalogues), but as best I can figure, they were terrified of losing their ability to produce rifles due to the Germans losing international priviliges left and right. As it happened, their stalking rifles and double guns were unaffected, but they'd both put a lot of effort into the design of their new shotgun, dubbed the Nummer (Number) 126, as well as produced actual examples. It got to the point where they was simply no turning back. And the Remo Nr. 126 was quite successful...over 100,000 were sold between 1919 and 1932, but the company started having financial problems due to a combination of unwise spending in the late 1920's and the stock market crash. The Geha is a little tougher to figure out. It's clear that it was a competitor that was produced beginning after the D.R.P. on the Remo Nr. 126 had expired, but no one is quite sure who first made the Geha. Several companies put them together...most notably Rheinmetall and for a time after the Depression, F.W. Heym (of all manufacturers) seems to have made them.
"Are these not German military firearms that were de-militarized by the conversion into something that could still be used under the treaty's supervision?"
Well, that's the thing...to demilitarize a Gewehr 98, all you had to do was remove the rear sight and lengthen the chamber by three millimeters. THAT is actually a very common conversion you'll find if you hunt around the German sporting rifle market. Most '98's were demilitarized by turning them into sporting rifles.
Most of the Gehas seem to have been made on a huge group of unused 1916-1918 Spandau receivers subcontracted by either Pieper & Co. of Liege or Siemens & Halske. It was long thought that Gehas were actually made by these two companies, but the discovery of a handful of original Gewehr 98's bearing the same markings has changed that line of thought. As opposed to forced demilitarization, it was more likely a marketing ploy at first (and then, in the early 1930's, an excuse to keep Germany's arms factories running at full speed).
"Additionally, the metal in the action is exceedingly thin to allow for the 12ga barrel, and the locking lugs of the bolts are barely engaging on them."
Not quite. The frontal locking lugs don't enagage AT ALL. They don't need to. The Mauser 98 action was designed with a third lug, sometimes called a "safety lug," engaging just fore of the trigger. It may not seem like much, or sound like much, but that safety lug can handle significantly more than a typical American bolt shotgun from the period. It can handle over 15,000 PSI repeatedly. A 12 Ga. shotgun shell produces around 10,000. As for the action thickness, while it would be extremely dangerous with a rifle cartridge, again, because of the lower pressures a shotgun shell creates, there is no inherent danger.
"As I understand this to be true,(at least in the case of the ones I've been shown) Please tell us their origins, and what weaknesses we might encounter that would cause us to lose an eye."
How to lose an eye...either overload the gun (because even the "mighty mite" safety lug will blow out if you start loading the gun with baby magnums or 3" shells), forget to watch for a cracked lug (not caused by repeated pressure, but rather survival from an overload), forget to put in a short (2 1/2" is what I recommend) shell or, and I stress that this the most, foretting to MAKE SURE YOUR BOLTHEAD IS SECURE. Because the nice folks at Remo-Gewehrfabrik reinforced the bolthead with a screw, you've little to worry about there. But Gehas and Hard Hit Hearts rely only on spring tension. If the spring snaps (almost without exception on ejection) and the bolthead is ejected with the shell, the gun can still fire. If someone sticks another shell in there, well, you're gonna get the backblast from the primer in your right eye.
"I would not buy or sell one of these, knowing they could easily chamber a deadly load through operator error."
I'll admit, they're not shooters for everyone (although more for their extreme clumsiness than being dangerous), but if you ever find a beater, they do make nice wall-hangers and/or conversational pieces.