Program hangs/circuit saturates once ICD3 is disconnected from PIC16F819
Thanks so much to Andy aka for helping me eliminate potential causes! 

The real reason as to why this occurs is due to Microchips "Low Voltage Programming" mode that is a part of the PIC16F819 architecture, and the fix is explained in more detail here.

The fix, according to the post, was to ground the PGM pin with a 10k resistor (I grounded it outright and got it working).

Alternatively, as another poster in the same forum notes: is to set ICSP to high voltage (via the configuration bits), disable the LVP pin in code (which wasn't necessary for me, but I'm leaving it here as it was contained in the original post), as well as putting a resistor between VDD and the MCLR pin.