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

Why? Planning the most power on a budget. Perhaps iron906 or 346 heads would get more flow than entry level ($550) assembled aluminum heads that are then ported.
Because not all OE heads are created equal or port out equally. Then there is the variable of valve size choices and there dimensions. So let’s start at the beginning.

I’ll skip purchasing the OE heads cost and assume you or someone else reading has a set on there engine now. The cost of rebuilding and porting an iron head will more than likely be more expensive than an aluminum head. The condition of the head is a variable to start with and what’s done to it is another variable. Then add the porters cost.

IF you purchase a set of TF or other heads of a good known reliable and trust worthy source for there quality and air flow reports, it will more than likely be the best and most cost effective way to simply bolt on power.

You already have the heads now BUT porting them may not be the cost effective route vs a reputable set of CNC heads OOTB. Something like a Black Friday sale and then worked on would more than likely play into your favor.

Just look back to the multiple “C” program I listed earlier.