Edit: It seems the Beckmen and Mr. E versions are one in the same.
For others looking to understand the differences between these edits, here is a summary as I now understand them:
Alien Appendix 2: Virtual Workprint:
Pretty much a re-issue of Alien Redux (another fan edit) that utilizes all existing footage from multiple DVD releases. Upscaled from letterboxed to anamorphic.
Some of the added footage is raw audio recorded on set. Some alternate audio (lower quality and without effects) has been used (occasionally replacing finished audio).
Looks and sounds like a workprint. This is for the person who wants everything known to exist.
30 minutes in, I'm thinking of quiting because it's a bit rough to watch.
Alien EE (Mr. E (Beckmen?)):
14 minutes of added footage. All sourced from the Quadrilogy's 2 cuts and the deleted scenes on the second disc (converted to anamorphic).
Alien EE v2:
The above edit with an extended version of the cocoon scene and some audio/musical fixes.
Moved the cocoon scene to before the self destruct is set (considered the original intended location for this scene (* see below)).
From what I can tell the finished/polished version has been replaced with the raw footage. As described by Imdb:
(The scene) originally opened with flat, static shots of Ripley clumsily descending a ladder, now opens with a low-angle tracking shot of Ripley descending much more smoothly.
Alien Hybrid Cut (LeoneNut):
The theatrical cut was used as a foundation and most of the added content from the Director's cut has been added (minus a scene that shows too much alien too soon, and a 2 second bit with Jones the cat).
The cocoon scene is move to before the self destruct is set.
No additional deleted footage was pulled from other sources.
*While the cocoon scene may be thought to be more appropriate BEFORE the self destruct is set, in both the Director's Cut and raw version of the scene the self destruct alarm can be heard in the background.
Did I miss anything? I'll update this post if anyone has anything to add (perhaps I'll copy this to the first post for information purposes).