Have not seen this one before - A SC with bridge rectifier!
So, heres my (confused) understanding..
"The instructions say my first testing point should be TP GND to TP1 and the reading should be around 9V. My reading here is 19V. "
This is the output from the regulator to GND - this result says that, if the regulator is correctly connected, it is dead.
"When I test from TP GND to REG 1 I get a reading of 42.5V in to REG 1, and 17.5V out."
Now the above is incomprehensible to me - beacause you say "and 17.5V out" - But if by "out" you mean the output of the regulator - well, this should be connected to TP1, which you just said was 19V...
As for the "I get a reading of 42.5V in to REG 1" - If this is true, then you have destroyed all the electrolytics before the regulator..
"When I test from TP GND to the power input it reads 21.5V."
Well, if you are seeing 21.5V AC input, This should give you a little more than 30V DC .. still doesnt explain the 42.5V..
1.) Dont connect power to the board again! ;-)
2.) Replace the electrolytic (470uF 25V)
3.) Ideally, check the diodes (use ohms - they should conduct one way only - Google "testing diodes with ohm meter")
4.) Replace the regulator.
You might have blown the whole board up - It may be that the regulator failed short-circuit - it may be that some other components are pulling the output down... Or, you may be lucky.
Oh - Nearly forgot.. Replace the transformer ;-).. But check its output voltage BEFORE you connect it to the circuit! No more than about 16V AC should ever be put into the supply socket.
To be honest, this is by far the crapiest SC theremin schematic I have seen .. 12V AC is way too high for safe design anyway - You need 12V DC into the regulator, 12V AC rectified gives about 17V, but tolerance on (particularly unloaded) transformers is abysmal - You can easily get 16V, which cranks up to about 23V DC - and with capacitors rated at 25V that is way too close!
My advice would be - Pull the diodes, and feed the theremin with a good DC 12V from a regulated wall-wart.
"Any ideas how I can get the voltage down to 9V between TP GND and TP 1? "
With luck, if you follow my advice, you will see 9V (from a new regulator).