Your notes raise some fair points, though I don't see your version as correcting them, or really having much connection with my version or as better meeting what I believe should be the criterion for assessing the introduction:  
 "rate of increase of actual, intuitive understanding of GA (as distinguished from CA by its applied nature) in a target audience with high school/undergraduate-level knowledge of math and physics". Your version has even more of the problems I mentioned recently in the talk page than the current active GA article, and it wouldn't serve any purpose to address them point by point since the new version simply runs completely against the goals of the first draft. It's not really a revision but a different proposal which seems to have completely different goals and a completely different audience in mind.  

 No doubt you meant to add your proposal to the talk page rather than substituting it, so I will add the first draft back. 

 On jargon in the old version: "(degrees of freedom/axial vectors/weighting coefficients/hypercomplex number)". I can't think of a better concise term than "degree of freedom" - a wikilink should allow seeing what is meant if it isn't clear in context, which I think it would be for most as:  "something that it takes a real number coefficient to describe". What would "Dimension" would give the wrong idea entirely. "Coefficient" would confuse the thing and its representation, and be too coordinate-linked. What concise term do you think be clearer?  

 "Hypercomplex number" was also, I thought, quite clear from context as "something like a complex number but with more parts", which is good enough for a first understanding of multivectors, an analogy that turns out to be more than an analogy. "Coefficients" is scarcely jargon, certain to be known by anybody who has done algebra in school, though "weighting" could be taken out. "Axial vector" could easily be left out, but in context the naive reader will see that it has something to do with rotation and magnetism and that GA uses bivectors instead. Anyone who has had freshman physics in college, or even most good high school classes will have come across axial vs. displacement vectors, and it's a good opportunity to bring it to the attention of the rest, because using bivectors instead of axial vectors is perhaps the biggest single advantage of GA.  

 There are two ways of making the draft better - changes and additions. Changes that simplify and clarify are the best changes, but additions are better if the point can't be made in a revision without going into a digression or other interruption of the flow. One can't say everything at once, so an order of presentation is needed, and getting into details or using more technical and more difficult terms should be deferred to later parts of the article, so that an clear initial overview of GA can first be presented to give the reader a schema for mentally organizing later, progressively elaborated parts of the article. That's why I didn't get into  all the various equivalents to complex numbers, instead giving as an example negative signature basis elements. Signatures are explained so early primarily in order to introduce the quadratic form / space in its concrete application rather than as just a term, and to introduce the idea not only that there can be many different varieties of CA/GA, but even conveys a pretty good implicit idea of how they are classified and distinguished. These initial understandings can be refined or generalized later. 

 I'm not opposed to the mention of related mathematical concepts and terminology in later parts of the article, but they should preferably be explained in terms of GA concepts (rather than the other way around), and the GA concepts in turn need to first be explained and understood by the reader using physical and geometric intuition, if possible, or the most widely-known levels of academic knowledge - e.g. high school algebra, not college-math-major abstract algebra.