There may not be a good alternative to potassium bromate in the home kitchen. Vitamin C (ascorbic acid), as you noted, is used as a replacement as it is a natural oxidizing agent, however, it requires oxygen to work and even then has other shortcomings not the least of which is that it acts faster than bromate. To get oven spring and tenderness with ascorbic acid that is comparable to what bromate can deliver, you would probably also need to incorporate both oxidative (such as glucose oxidase) and carbohydrase enzymes (such as fungal alpha-amylase). The first to provide oxygen, and the latter to compensate for the faster action and improve the oven spring and soften the texture. Getting these right would be daunting to say the least without a lab.
You might give long fermentation (24 hours+) time a try. I'd give it a try with and without (using greatly reduced quantity of yeast) refrigeration.
I'm assuming you are using regular yeast (active dry, instant dry, or cake) correct? A sourdough culture might also give you interesting reesults to experiment with.