Rob, two things:
1: In the diagram you have drawn, there will be essentially zero flow though the heater core, as there is no pressure differential across it.
2: Any coolant you take out of the front of the head is coolant that the rear of the motor is robbed of.
At a minimum, you need to route the water which is exiting the heater core to the inlet of the water pump (lower radiator hose), in order to promote coolant flow through it.
It would probably
also be beneficial to source water for the heater core from the back of the head, post-thermostat, and block off the front outlet. Essentially, just put the heater core in parallel with the main radiator. And having done that, make damn sure that the heater core has good airflow through it so you're not creating a non-functional bypass around the radiator.
(I assume that you are free to relocate the heater core to, say, an upright position protruding through a hole cut in the hood.)
Actually, I just had a brilliant idea. Or maybe a dangerously idiotic one. I'm, not sure which.
Go out and scavenge a dozen heater cores. Place them on top of the hood, upright. Eliminate the main radiator altogether, and plumb the opening in the front bumper straight to the intake (poor-man's ram air induction.) Work the theme of the car around the dozen heater cores on the hood. Maybe put little Barbie heads on them or something.
Grille of Damocles be damned.
(Wait, you said Chump Car, not LeMons... Well, think of something.)