VREG output circuitry
Your architecture doesn't make sense from what you are saying.  Combine the two power sources before the regulator, not after.  The transformer with full wave rectifier already can't be back-driven due to the diodes.  All you need is a Schottky diode in series with the DC barrel connector.  That's a good idea anyway to avoid damage when someone plugs in a wall wart with different polarity.

Combine the output of these two power sources right there.  Now you only need a single regulator, which gets around the awkward combining of the power after it's already at the final voltage.  If the wall wart and transformer output voltages vary a lot, use a switching buck converter.  Those can remain efficient over a much wider input voltage range.  If you really need extra clean linearly regulated final voltage, have the switcher make a few 100 mV more than what you need and use LDOs at the point of use.