Soundproofing basement ceiling..

The soft tiles you mentioned in your drop ceiling provide some insulation, but if you want more I think your only option is to install fiberglass batt insulation above your drop ceiling.

Oh no....you have many more options than fiberglass batts.
Firstly, you either want soundproofing or you want cheap NON-soundproofing.
Remove all the drop-in ceiling tiles.
If you have a concrete slab above you need to attach 3"x2" wood battens to it through special rubber insulators. Then fix 3" fibreglass insulation between the battens before fixing 2 layers of 5/8" plasterboard (Fyrchek) to the battens making sure no contact is made to the walls at the ceiling junction. Fill this 1/4" gap with silicone sealant.
If you have timber joists above, the best way is to span a separate timber structure to support the same ceiling as described above.
Alternatively you can attach timber battens cross-wise to the joists again through special rubber insulators and repeat the ceiling structure above.

I just want to add one thing to the mix.

I tried to stop the music from the basement using fiberglass insulation and styrofoam sheets between the rafters, and then the acoustical ceiling panels to finish everything off.

I finished the whole basement and turned on the system. Guess what? The sound still came right through.

Breaking down what was happening, I found that the sound was coming up through the heating vents.

Chuck

There are some products especially made for heating vents to stop some of the sound. Also, it would pay to put the air handlers on shock mounts. In the end lining the ceiling with lead paper might be the only way to go. I did a room many years ago and used lead paper to great effect.