A little rental stage 101 if I may
Since the film was suppose to be sixty minutes (or even if it was 90 minutes) the shoot should not take more than 15-16 days to film in the studio using a standard break down of the shooting schedule. Their actual rental only costs should never exceed 50K IMO . The real money comes in on the crew and construction of sets. A good scenario would have been for them to rent the studio for 20-22 days to allow 5 days for set construction/pre-production, then film for 15-16 days*, then allow 2 days to strike the sets, dispose and clean up the rental stages.
* Keep in mind you are always building or refining sets even while filming for a this type of production.You start shooting on your easy to build sets and/or green screen near the beginning. This allows time to get more complicated sets done and shot late in the production. We had to do this, and also have multiple set constructions going on at the same time to maximize efficiency and time management.
The production has to be a well oiled machine, if set construction gets behind that could derail the entire production, especially when you can only get certain actors on certain days. A good producer MUST, I repeat MUST, have prior experience doing this and work his way up for that role! If he does not, he needs to hire a professional producer that does .
Again, as for rental vs. permanent studio for Axanar, with our a doubt he should have rented a studio and shot the dam film. He would have a had so much more money to get everything done at a professional level.
If he was worried about sets, or how long they would take to build. he should have rented very cheap warehouse space for one-six months (depending) before the shoot, with access to a loading dock. Have the sets built there in a way that can be broken down for portability. Then, when they shoot the film, they drive the set pieces over to the stage and set them up in very minimal time. When they are done they have them stored at a storage faculty (cheaper storage than a warehouse or stage) until needed for the sequel. This would have been one of the better ways to maximize time and money. You just have to be smart about what your doing.