Have you read the whole thread? It's quite clear to me that very little measurement went into designing the typical BFI for ideal airflow. As I said above, it works by blind luck, not by science. That tells me it can be improved upon.
Right from the start, the "B" in BFI tells me it's an erroneous approach. Big has nothing to do with why it's an improvement. The stock snorkel is sufficiently big to provide as much air as the intake tube behind the filter can accept. It's actually 50% bigger, so you could get by with a smaller than stock snorkel and have the same performance as the BFI. It just needs air from a pressurized source. That's probably why Lexus put in an oversized snorkel, since that's low pressure air behind the headlight. That also keeps the filter clean and dry.
Opening up the airbox for a large volume is not the answer. At least, not in anything but a sledgehammer approach. If the BFI were better thought out, it would just be a tweak to the stock snorkel, routing its open front end over to the radiator cowl flap. Admittedly, that's a very tight space to work with and options are limited. Which is exactly why I started this thread to discuss better ways of doing things.
What happens if that radiator cowl flap that is being bent out of position to supply high pressure air somehow fails, either from the bolts loosening up or the plastic itself cracking at the washers? It is subject to very high wind forces in a manner it isn't structurally designed for, after all. Suddenly, you're choking the engine of all airflow, since you've sealed off every other entry point. That's why I said I'm not fond of that approach. If I end up pulling air from there, it'll be with an actual hose dropping down into the bumper opening.
I haven't yet come up with a good plan for how to pull air from the right bumper opening (the intercooler area) and up to the stock airbox without a lot of sharp bends back to the front of the box... There's something workable there, I just haven't settled on what yet.
I'm thinking dual 2" pipes straight up from below, lining up with the bottom of the box. That's just enough space internally to clear the filter. What it would do to airflow characteristics in the box, though, is a tough question. Once pressurized, maybe it doesn't need to point straight at the filter? Dual 2's is a bit on the light side, so I would probably supplement it from an additional hose or two over from the radiator cowl. That should exceed the intake hose's volume further down the line.
I'd also need to cut a new panel to glue in for sealing the stock snorkel on the front of the box, otherwise all that pressurized air just hits the back of the headlight.