I am very happy to report this...for so long I have been lamenting that I cannot make gluten-free bread oil-free very easily. I've had a lot of bad experiments...however, I have been experimenting with adding grated zucchini to my bread. I made some cornbread and I added too much water-it didn't cook properly. But, today I cooked a regular loaf of bread with less water (and less sugar, thank god), and it turned out quite well. I still have to tweak the water content, but I see this as a grand success. I added about 1/2 cup grated zucchini.
In the future I will experiment with adding squash and perhaps potato to recipes, to try to make them "whole food" breads, that is, so I don't have to add starchy flours, instead add the whole starch themselves. It might work!