Hi TIMBO!
I checked out MC78T12 datasheet:
http://www.datasheetdir.com/MC78T12+download and it seems to have less ripple rejection them LM7812 series. I have never tried these though.
A few observations which might help.

1) 12A_7 series eat ~150mA when running @ 12V. That implies 750mA. I would use UF5408 (3A) diodes to rectify AC since UF4007 is rated @ 1A. Ample margin for safety reasons;
2) I highly recommend using a big hokkin heat sink (at least 2"x3") with thermal grease. Just a very fine layer of grease on both heat sink and reg chip;
3) To sim load, you will need 16ohm/9W resistor. 2x8ohm/10W (series connected) will do fine, but it will get blistering hot. Watch your fingers mate!;
4) Keep track of chip temperature while you power it up. On my first attemp, reg chip temp skyrocketed seriously fast;
5) I don't know whether you own a scope or not but if so, when probing regulated output voltage from chip, try paralleling more reservoir caps (big 4700uF e-caps) to see how much your filtering will improve. On my last attemp, I had to go from 2x4700uF (200mV pp of ripple) to 7x4700uF to get ripple down to 50mVpp;

I also recommend that you do yours on protoboard first, them move it to pcb;
6) You might want to try some small caps (use a factor of 1:100 or 1:1000) to scale your caps. it will improve a lot of high frequency garbage riding along with 120Hz fundamental.
Hope this helps you. And if I can help you further down the road, you are welcome mate!
Best Regards
R.