Bit of a flaw in the game
imo.
As long as you stay within budget and achieve what is expected then thats all that should matter. Solving a clubs financial trouble is not the job of the manager
imo, but of the board.
I'm having a similar experience at Kettering. I won the BSN in my first season, didn't spend any money,sold some players and stayed well under budget and had the largest average attendance in the league, but I still lost money every month.
Currently in BSP, mid table and still losing money
However, the only realistic options(apart from the obvious one of selling all your players) are:
1/ Mutually terminate contracts of any extra un-needed staff(do you have 2 physio's?)
2/ Offer all players and staff reduced terms, many will accept slight decreases in my experience.
3/ Arrange friendlies/cups/tournaments and invite higher reputation teams.(arrange as many as possible)
4/ If you do have some players to sell, add a % of next sale to the fee,even if only 10%, most teams will still make an offer. This may help a little bit in the long term.
Sadly this may not be enough unless you can get yourself into League 2 and start making some decent cash.