Here is the dial for my VE:

Sorry for the previous CH Meylan picture, I took it from archival pictures from an Ebay auction and would like to give credit to the original seller SFLMAVEN. Yet another Gruen in my collection with picture, this is a V2 19j chronometer balance in the same series as Rob's V3:

Ben, I don't know what the most common thin Meylan movement design is. I have about 20 Meylans. Scarely any are exactly the same. I have been trying to find a pattern that will explain the variation, but without significant success.

The Meylan movement you depicted is very close in appearance to the one I own shown below. You are correct in describing it as a very thin Meylan. The movement shown below is 2mm thick. I have a dozen Meylans that are between 2-3mm thick, but this is the thinnest.

Note that this movement, and the one you showed, both are discretely marked with a Cress Arrow insignia.

To add to the Gruen information: My one and only Gruen is a SemiThin model with a Gruen 758 movement with 15 jewels and adjusted to 2 positions. This was a lower end model for Gruen in the 1920s, but still a quality watch. My image is only a scan so the quality leaves something to be desired.

Adding to the pile are my 3, the 19 jewel on the left a recent addition, for the best MONEY ($17) as it was advertised as an "Elgin". the model and right hand ones are mid-grade Verithins and the Penta is a 14K solid case, so it has some value, I suppose. Serial numbers and description (L-R);
S/N None signed "Watch Specialties Co., 19j, 5 Adjustments", early Gruen <1915>;
S/N 473546, 17j, Adj 5 pos., Temp. Verithin Precision, "Octathin" Gf Case
S/N 531109, 17j "Temperature Adjusted" Verithin Precision, solid 14K Gold Pentagon Case

The movements all look like they are in the same family.

thanks Ron and David for showing your Gruens. Ron, is it possible to see other pics of your Gruen's movement and case? If not, what's the serial number and inscriptions on your 758 (including personalized engravings)? David, you have 3 nice and interesting Gruens here. First one is a SemiThin movement with DGS logo to indicate that it's an older piece. I believe you can get the S/N underneath the dial on the top plate. From bridge design this caliber is a 740. The other 2 shaped watches are V4 movements, the octogon one is probably an 'octothin' model and the pentagon one is very nice in 14k with precision movement. It'll be nice if you can elaborate on any personalized engraving and case number etc. Thanks for sharing guys.