FYI -- Test with heat sink was successful -- yay. I modified the original post and reported the thread as solved.

I feel very inexperienced at this point -- Duh!

I assume ground tying and UBEC will also work.

Thank you both again for your help

Techpaul, would it be reasonable to link the R-pi ground to the 12v ground via the gpio pin? That seems easier than trying to splice via the wall adapter supply or at the mini-usb port.

Joan, I also ordered a UBEC to play with.

Thank you both for the help.

I will add a heatsink and report back, or, do you think the energy dissipation is just going to be too great so as to be insurmountable? Seems it should be doable since it is a 1A rated regulator, so, there has to be some way of using it. I desired to use the regulator because I have a string of con...

It works off the mini usb power supply with a wall wort, I believe 1A, but, it works, so, whatever the rating, it is enough. The 5V to the GPIO pins is run off a fairly beefy 12V supply regulated down to 5V with a 7805 with appropriate caps -- since these are only $4, I use these: http://numato.com/...

look in /etc/resolvconf/resolv.conf.d

there should be a file called base that might get added to the resolv.conf file on reboot

throw in a line like:
nameserver 8.8.4.4

Solved Symptom: R-Pi with wifi using power supplied to the GPIO pins via a 12v supply regulated down to 5v with 7805 had many issues (wifi fail, crashing, etc). Cause: 7805 without heatsink overheats leading to voltage drop and subsequent R-Pi failure Solution: Heat sink on 7805 works, additional su...