This is a lesson for all those people who think that Canada is just like the United States - only more boring (or less likely to wage war, depending on your political leaning). The all-powerful Canadian Grain Commission has decreed that your white flour shall have 13% protein, of which 12% is glutenins and gliadins and one percent is water-soluble albumin. The United States, despite its inclination to tell other countries how to manage their affairs (or heartily encourage them, again depending on your political leaning), does not tell its millers how much protein they must mill into their flours.
Yes, our bread flour consists of 12% to 13% protein, but our all-purpose flour can range from 9% right up to 12%. Indeed, our favorite, King Arthur All-Purpose Flour, proudly states that it is milled of hard wheat to a consistent protein content of 11.5%. That’s not too far from your grain-commission-decreed standard. And may we, in all modesty, say that our banana bread is delicious and not the least bit gluteny.
Our guess is that you’re either using too much flour, you’re mixing the batter too aggressively (which causes the rampant formation of gluten), or you have a questionable recipe. If it’s a recipe you’ve used before and loved, try decreasing the amount of flour by one tablespoon per cup used, mix it gently once the flour has been added, and see if the result isn’t substantially better. If it isn’t, we’d look for another recipe or try your suggestion of blending cake flour and all-purpose flour (but we would do so without letting the Canadian Grain Commission or the U.S. Department of Defense know about it).