The first thing you should do is apply for 3rd Mate. Since you have taken the same exam for Mate 1600, you may not need to take a new exam. You will receive a tonnage restriction on your license, perhaps only 2000 GRT / 4000 GT, but at least you’ll have the Third Mate license in hand. It may take six months for NMC to process your application.
Then you can work on getting seatime to remove the tonnage limit.