Oven spring is caused by the air pockets in the dough expanding from the heat. (Dough rises from gasses released from the yeast.)
After the shaping and final rise, often times there is a light, dry "skin" over the dough. By slashing a dough before it goes into the oven, you break this skin, and the bread is able to expand. If the loaf is a "fancy loaf" and you can't slash it without ruining the appearance (like a braided loaf), try to keep the loaf from drying out with a light mist of cooking spray after shaping and before the final rise.
Perhaps the bread is cooking too quickly when it hits the heat of the oven, essentially cooking a crust before the air pockets get heated enough to expand? Baking in a moist environment should help with that. Place an empty, sturdy pan (I use a cast iron skillet) on the bottom rack of the oven (or directly on the floor of the oven) before preheating. When you place the bread in the oven, pour about 1 cup of very hot water into the empty pan. This will create a bunch of steam, and help prevent the bread from crusting before it gets its "spring."
If you have a pizza/baking stone, use it. Having a hot surface to set your pans on helps with the rise. Think about it... you open the oven door, and out goes a lot of the heat... even though the walls of the oven are retaining the heat, it will take a little while before that heat reaches the bread. Setting the pan on the stone will give you that instant heat on the bottom, causing dough to rise from the bottom up, rather than just getting a small rise from the top area.
If you don't have a stone, invert a heavy baking sheet, cast iron griddle, or something similar, and heat that up in the oven the same as you would for a baking stone. Invert the sheet pan so it's easier to slide your bread pans on and off the hot pan without having to deal with a small edge.
If you haven't got equipment to do the other options listed above, you can try the "cold oven method." Just put the loaf into a cold oven, and set the temperature. Don't preheat. The gradual heat from the bottom of the oven as it preheats will give you some of that "oven spring."
I use a baking stone and steam, but I have had great success with using an inverted aluminum sheet pan with steam before I got the stone... and before I learned that trick, I used the simple cold oven method (no steam as the oven is cold!).
If I were to convert a machine kneading time to hand kneading time, I'd take the time and at least double it, perhaps between double and triple, depending on how strong/vigorous you are.
The odds of over-kneading by hand are pretty low, as compared to by machine.
I would guess that the flour substitutions or the coldness were more of an issue than the kneading. I've not heard of this book or either of the flours mentioned, but I do know that mileage can vary a LOT with wholegrain flours, and even basic white flours depending on where you live, due to changes in protein contents for regional differences.
Best Answer
Allowing dough to rise twice results in a finer gluten structure than allowing it to rise once. It results in a smaller crumb and prevents huge gaping airholes in your bread. The reason that you have to let it re-rise is that you just pushed all the air out with the kneading you did developing that gluten structure.