If possible, connect your LED strip (or strips) in one long ring, with both ends going back to the power supply. Now connect the positive of ONE end of the strip to the supply, and the negative of the OTHER end of the strip to the supply. You're not "double ending" the supply, you're feeding positive from one end and negative from the other.
Now as the LEDs get further away from the positive connection, they're getting equally closer to the negative connection. The overall length of copper for each LED is equal, so the voltage drop should be equal, with no visible dimming at the far end because effectively there is no far end.