I'm not exactly sure what that means.
The nameplate of a delta-wye transformer will show the vector diagram for the H1, H2, H3, and X0, X1, X2, & X3 connections.
I don't know what the unit stickers are.
Again, just swapping the H cables around on the H terminals will not cause a fault. (Swapping any H to X leads will!)
When you say it immediately shut down, I'm assuming a C/B or a fuse opened, and there was some noise/arcing in the transformer, etc?
Can you explain "the taps in the other two windings seem to have hardwired themselves in its maximum setting" better? Usually, a transformer will have five taps (one for nominal voltage, two above and two below nominal)which are adjustable for each coil by means of a jumper wire. What size transformer and what voltages are we dealing with?