There is a huge problem with any reimagining of Stargate that wants to be grittier or more solemn: The basic premise is completely stupid. Every effort to reimagine SG-1, from the Ori on, broke on this fundamental problem. The viewer can accept the nonsense with willing suspension of disbelief but then he or she cannot simultaneously mentally engage with the supposedly serious drama. The car is either in idle or in high gear. You might keep it up for a two hour movie, but most people's minds wake up for the commercials. (I hope.)
On the other hand, SG-1 was a very successful action/comedy show. It's premise was "We came, we snarked, we conquered!" All the elaborate mythology was just clever writing.
In other words, a reimagined SG-1 should aim for revamping the comedy matrix.
Step 1: Re-do the discovery of the stargate as a civilian project. The original civilian team under Dr. Samantha Carter goes through, falls foul of Ra. When Ra sends troops through the gate on recon, Gen. Hammond sends Col. Jack O'Niell through. The hardbitten soldier saves the civilians and establishes a base on Abydos for further investigation.
Step 2: The new base discovers that Ra wasn't the only one and the key to the gate system. The military can't take over the project because they lack the expertise, so the military has only limited authority and limited resources in the new search for the gatebuilders.
Step 3: Further develop characters and mythologies by stand-alone episodes. If they are decently written the characters will be defined by their actions. And if the writers are half as clever as the original crew, a fun mythology will grow.
But it all depends on the casting and the comedy matrix, as you might call it. G.W. Bailey for General Hammond I think, and Stephen Lang for Col. O'Niell. Tony Shalhoub for Kasuf, to play off Hammond as local leader. Lang would do the badass ticked off at the sloppy civilians who have the upper hand over the tech. Dr. Carter would be an older actress who can do no-nonsense (Sigourney Weaver would be ideal, but maybe Janeane Garafolo) and play off Lang. Dr. Jackson could be gay (Sean Maher, yes, that could work) and really play off Lang. The teams going through the gate would vary, with military members including Kowalski and Freeman, with locals like Skaara and Share insisting they share (like the Russians in the original series.) These would be played by relative unknowns. Dr. Frasier would be a biologist from the university mounting the expedition. She would be friendlier, more tomboyish (culture clash with Abydonians,) maybe played by Amanda Seyfried in Jennifer's Body/Gone mode.
Standard missions would include a scientist, a soldier and an Abydonian "observer." The difference in viewpoints between the three sets would build in conflict for humor (and the occasional real drama sneaked in for variety.) Deemphasizing the physical stakes to Earth would decrease the need for storyline megalomania.