I recently changed my strings to a larger gauge (from 11's to 12's)
and did a tune up/truss rod adjustment.
During the intonation process I encountered a situation involving the 3rd (G string) and 6th (low E string) not having enough adjustment room to achieve correct intonation (sharp when pressed at 12th fret). In other words the saddles are backed up against the back of the bridge plate and will go no further.
Most likely operator error What did I do wrong?

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This is not uncommon.

With Strats, cutting the length of the spring or removing the string altogether usually solves the problem. Lowering the angle of the tremolo block/plate helps too.

With ABR-1 bridges, only a few have good results with turning the affected strings bridge saddles around. This is why Gibson came out with the Nashville bridge as a replacement as the Nashville has much more tracking distance in either direction.

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You dig?

I'd go with removing the string and pretending its a 5 string bass

shorten the spring.