The green glue with another layer of 5/8" will reduce the noise level, but it will not solve it to the level you would be happy with if the clarity of the speak is that clear in my opinion.
Without knowing the exact wall insulation / sound proofing between the 2 units, and truly knowing if it is gapped double wall or if it is a single wall with 2 layers of 5/8" drywall, one on each side you can't even begin to comprehend how well sound travels through a floor system. The place I am in is one single deck with the 5/4 x 6 floorboards (construction today uses plywood) running from the unit next to me into my unit. Next door they just refinished the 145 year old floors, and I did the same, when you drop something on the floor like a quarter, sounds just like it was in the same room.
I hate carpet, so I installed a padding with an engineered flooring on top, the difference in massive, another reason people like carpeting for the sound deadening.
But sound will also travel through the wood studs, thus gapping and breaking the bridge is important. All the times I have used Green glue, it worked ok for the mid tones, but nothing on lower base tones and some higher tones, thus you still heard everything, just not so precise.
I got my best results with gapping and safe and sound from rockwool, and then the Mass loaded vinyl barrier before sheet rock, the Mass loaded vinyl barrier breaks the path of travel from the wood and dulls the sound passing through the voids (insulation zones) besides the wood studs, then 2 layers of drywall.
If the sound is that clear with a STC of 30, getting to 45 might be an improvement, but the STC is mainly the mid tones, so the highs and low are normally still pretty clear when sitting near the wall or rooms without carpeting.
That is what happens when your neighbors are that close and the architectural plans are figured for the basic minimums.
Not sure what your options are, but I would look at all of them before pulling the trigger and not being afraid to try and work out getting a better level for more money, I have never been happy with STC 45 levels.
Then again I like it quite.....