Hollow wall green retrofit

I have an old house with brick exterior and wood interior. Between the two is an air gap. Modern conventional wisdom says to increase the heat efficiency we should stuff the gap full of insulation. However, I noticed in summer that gap created a breeze way that drew the hot air out of the gap, leaving the house cool. So, if I fill in the gap, I might need less heat but more air conditioning. Talking to friends who had this done, they confirm, insulation holds summer heat.
This air gap extends into our floors, so when I feel penetrating cold, it's inching from the floors.

So I'm trying to figure out what to do. I know in Europe they are trying this inside wall insulation. I'm wondering if I couldn't cut the edges of my floors open and just fill the gap there so the outer shell of the house circulates different than the interior of the house... Would this make any difference? I'd like to get as close as I can to net zero without getting an air exchange contraption or something like that.

That air gap is there for the purpose of allowing moisture to evaporate and prevent mold from growing in the moisture.

Now a days they use a moisture barrier to wrap the entire house which allows this air gap to be smaller, but if you fill that space you are inviting a disaster by giving molds a perfect environment for growth.
If the house is older, chances are that the moisture barrier is black board or just "tar paper" neither of which work very well and thus the need for the larger air gap between the wood wall and the brick veneer.

To keep penetrating cold from infiltrating at the floor all you need to do is seal the gap behind the base boards, that requires removal of base boards, injection of expanding foam to fill the gap between the sheet rock and the exterior sheathing, and then replacement of the base boards.

Quick question...  Is the cold floor air coming in at the baseboards or is it traveling under the floor (between the floor joists) and making the whole floor feel cold?

Hi thanks! It's coming from the floor joists at the top of the basement, but that also happens to be where I can see in and therefore the air can escape. It's also got patch work of insulation where there were repairs and the walls are cold. I don't want to pull the whole place apart. I read a paper today that said interior insulation can be disastrous by creating a temperature drop between the insulation and the brick, rather than heating the brick, which in cold weather can lead to moisture build up and freeze thaw in the brick. Not sure I totally agree, but I'm in no knowledgeable position to disagree.

I'm not an expert on this so I won't distract the situation with my opinions.  I just wanted to make sure we understood.  If you can take a photo it may help to get you more input.

It's coming from the floor joists at the top of the basement, but that also happens to be where I can see in and therefore the air can escape. It's also got patch work of insulation where there were repairs and the walls are cold. I don't want to pull the whole place apart.

From this description you might have a couple of ways to stop the floor draft coldness. 1) you could stuff insulation between the floor joists, leaving the brick gap open for moisture control. (that paper you mention reading is absolutely correct.)
                                                                                                                             2) you could use spray foam insulation in the same place, then trim off any that tries to seal the brick air gap.

Either of these methods should give you a warmer floor and keep the integrity of the structure as it should be.

Redhawk