I can only add those things I've already added elsewhere around the forum. I cannot provide any proof to anyone of these things, but this is what I use in my own reading of charts. The Sagittarius A-star (SgrA*; galactic centre) is a distant, high-power centre of revolution. As our solar system is to our Sun, our whole galaxy is to the SgrA*. I believe that it does deliver more "power" than the Sun, but it is different in several ways.
The SgrA* is very distant, so orbs are effected. I allow only a 2° orb for it, but I don't consider the aspect to be tight unless it's within a single degree. Also due to the distance, I consider the SgrA* to act in a similar way to stars and outer planets. It "moves" in our sky at a comparable rate to the stars and it's influence is not "native," so to speak, to our solar system. It's a boost-of-raw-power kind of influence. There's no point in checking its placement, only its aspects. I pay the most attention when there are exact conjunctions.
In the month of my birth, Neptune was conjunct the SgrA*, with less than 0.1° of variation. I've seen the birth chart of another in which Uranus was conjunct the same, with the same exactness. It was certainly noticeable in personality, as well. Pay attention to aspects to the galactic centre. They matter.
