In regards to the current apartment:

Read through your lease agreement, if you have not already, and see if your landlord is contractually obligated to provide repairs. Also, there are a few states that have passed laws regarding the landlord's responsibility concerning mold. That said, this is arduous and time-consuming.

If you happen to have a very reasonable landlord, you may be able to enter into an agreement with them in which you do renovate the apartment in exchange for something like a free month of rent. In this scenario they would be able to charge the next resident more. This, however, will create a very precarious situation in which a contract will need to be drawn, vetted, and vetted again. So, not really viable.

Assuming that you will both have dissertations to produce and that the current environment is more of a hindrance than a benefit to production and study, a less cluttered and naturally lit environment may be the best choice.

In conclusion, do not renovate. This will likely just be money down the drain. Next, run the numbers. At $66,0000/yr, assuming the best income scenario you provided, you will have $5,500 a month (if that number is already reduced by state and federal taxes). Take out rent, $3,950 remains. Take out the price of parking and bills and then look at where the rest of your money is spent. At this point it should become clear whether or not the higher rent is really worth it. I have gone through this same decision and can provide more information if desired. I apologize if the above information is already too much.