Back to the OP and unrelated to winning/losing because in reality losing wouldn't matter. I'll let the other fine legal eagles figure out the why.
But OP you can expect to pay at least $1000 for representation and more if it actually went to trial. Whether you get legal expenses if you win depends on a variety of factors. Well two really, does a statute authorize it in this situation or does your lease have legal expenses clause. Basically you may or may not spend more money fighting the $1000 dollars than actually paying the $1000. It depends. No one on here can say one way or the other. It is why neither the landlord or the moving company are going to cave. They aren't going to take you seriously until they are contacted by an attorney that represents you.
If you lose, well I'll let the other fine legal eagles tell you about what would happen if you lose in a properly filed(for this case) lawsuit. I was arguing about you possibly losing earlier because its possible. It is always possible, more so if you go in unrepresented. The questions everyone should ask, especially you legal eagles, does it matter if the OP loses if the case is filed correctly and all parties are involved in the suit?
OP, sorry for being passive aggressive. It is not you, it is them.