I'm an industrial electrician and deal with 480V 3P most every day. I'm having a little difficulty visualizing what you are intending to do.
First, whether your 480V 3P incoming power is industrial or residential, it should be a delta or triangle shaped circuit. Each leg of the triangle represents some kind of load, and each point L1 L2 L3 is a voltage source. Your L1-L2, L2-L3,L3-L1 voltages look pretty much normal for a completely unloaded circuit. There should be no ground connections on L1 L2 L3, BUT - EVERYTHING wired up as a load should have 4 wires - 3 phase leads and an equally heavy green ground lead connected between every machine frame and the box's earth ground terminal. It's suicidal to neglect the frame grounds at these voltage and amperage levels.
I don't understand the transformer. Are you trying to step down 480V to 240V for some things? If you have 480V coming in and most of your machines are 480V you don't need the transformer.
Where I work we occasionally build and repair industrial gear that runs on 240V, 380V, 575V instead of the usual 480V. For these jobs we hook up various transformers mounted on carts for mobility. Otherwise, all the rest of the dozens of machine tools and welders are hard-wired or plugged into the many 480V circuits in the building.
On any given machine, check the rotation direction immediately on all drive motors, pumps, fans, etc. If any newly-connected motor runs backwards, disconnect the power source to the machine, and reverse any 2 of the motor leads. DO NOT reverse your 480V distribution leads in the box or elsewhere upstream of other motors. :-) You adjust the phase of each motor to the source.
Don't neglect frame grounds and proper fuses or breakers. Occasionally at work someone will hose down a 480V outlet box. The explosion and fireball are very impressive, and a new outlet and a handfull of new 100-amp fuses is expensive. :-)
A clarification on the transformer's role might help.....