Can a 400BBM w/cheap aluminum heads compete/dominate against the street LS?

Follow 4 out of 7, 7 C rules and you can get it done pretty OK.

Carb
Cam
Converter
Cog’s (gear ratio)
Cubic inches
Compression
Cylinder head

I’m not sure where you stand with the cylinder heads.
A Torque Storm super charger is not to expensive. But the upgraded fuel and ignition costs can be difficult to add on top when the bottom line is a concern. Gap your rings to suite and keep it under 10lbs. Oh! You’ll make power! And then what RRR said, a light car.