With your things properly segregated, you can get rid of those that you no longer need. You can choose to sell them online. You can also sell the items through a garage sale. Either way, you will be able to come up with more money for the move.
After that, you would have more space to move in. You would even be able to pack your things with more ease. The best part is you would need less packing materials so you will get some savings. With fewer things to bring, you would also save on transportation costs. And then you would even be able to downsize the storage unit you are renting. If you finally clean out everything in the storage unit, you would even free yourself from the responsibility of paying the storage rental.