I have maintained several bird feeders for decades so I have some history of watching their habits. Some birds stay near the feeder while they feed. Others like to go to another tree to consume the seed. If you put out seed, that will attract even more birds than you have now. And, they will spread out even more to eat the seed so that they don’t feel crowded. The problem may get worse, not better.
I’d invest in good wax and keep it maintained. You may want to talk to the owners of the complex about your problem to see if you can get another spot or they can remedy the situation in some way.