Holy crap, you definitely worked that one out.
I don't think I would be able to compete with your knowledge regarding production or contracts (and that my English is not sufficient to write into detail), or you knowledge about who was who and filled what role.
Well starting from the original series, definitely two more seasons.
I do however think there would have to be more quality control regarding the scripts. It would not mean the series would go more serious sci fi with no room for comedy/banter to break up or add to the more serious and dramatic parts, but I would definitely like to see the more B movie esque elements being removed or reduced.
Edit: as someone else mentioned, there would be philosophical and moral issues to deal with but I would insist it would have been kept realistic or applicable and not become all moral preaching to the audience. (also would keep any religious undertones low key or favor towards any religion)
And of course keep the show as much action-adventure oriented with elements such as comedy, detective, mystery, and horror where it can work. (not blood and guts, just playing a bit on people's fear for the unknown for the sake of entertainment)
Also definitely less questionable character writing, questionable as in of poor or average quality. (there will always be two dimensional characters but writing characters stupid or foolish for the sake of plot can go to far sometimes)
If the money was there some more investment in the sets, props, and models.
Hmm, a second five year mission/series is of course something we fans would like to do but again it really depends on the financing and the ratings.
Would the show bring in the money to justify more seasons.
I also wonder what sort of impact this would have on spin off shows such as TNG, DSN, and VGR.
With the original series now lasting a few years longer (and not having an average third season), would people want the franchise to move ahead a century or perhaps a series about a different crew or group of people in the same era?
Also this also would radically change how the movies would turn out.
Would Star Wars still create a want for a Star Trek movie? From what I recall the wish for a Star Trek movie was partly inspired by that and of course fans wanting Star Trek to come back.
Well I can tell you two things, there would have been more quality check on Voyager, and I probably would not have gone ahead with any prequel series like Enterprise.
Not only that there would perhaps be need for a break in order not to exhaust the franchise and overflow the audience (I know, not the right word but I can't come up with the right word right now) with to much Star Trek.
I think the public at some point was as tired of the show as the show itself was.
Edit: There are a couple of things I do agree with when TNG and later DSN and Voyager was made; removing some of the more sillier and unfortunate more ridiculous stuff from the original show's universe/the Star Trek timeline in general to 'ground' the show more.
For one, less or no 'godlike' or 'genie' like characters. I know the whole explanation "Advanced technology would at some point come over as magic yadiyadiyadi.", and I don't rule out that very advanced knowledge and technology really could pull of some stunts that we 21st century people would see as magical but there is a point where even credibility takes so much strain before it breaks.
Also, I don't think we/the audience want to see more more characters such as Q who put humanity on trial. As if we alone have committed both acts of kindness and decency and also atrocities but other species get off because they are simply following their nature or some such reasons.
Real powerful aliens should also be really weird, with there barely being any similar points of reference for us and them. Sort of like what the Prophets started out with, not understanding linear time as they live in place with complete different laws of time and causality.
Also less time travel, over the years of watching various shows, reading various books and comics, and playing games with the theme I have come to discover that time travel is really difficult to pull off well.
If it can not be written properly then it is best to ignore it.
Oh and limited to no travel to other universes. I think the Mirror Universe was better off as a one time occurrence and not something that could happen on a more regular basis. (this should have been something very incredibly rare and extremely difficult to repeat, not doing serious damage to reality at worst or killing yourself in a creative new way at best)
Plus I think it was more interesting a premise for a show like Sliders than Star Trek, if you make space exploration to be so boring that going to other universes is more interesting then you are making creative/writing mistakes somewhere.