I too perfectly understand your concerns about feeding raw. I have very recently had a spell of this with mine and I too was nervous. This is why I chose a prepared raw meal in the form of Nutriment. Also, I do not have the freezer space and did not want to have raw animal products about the kitchen, particularly as my OH is elderly and immunosuppressed due to long term steroid therapy. I would recommend these prepared raw diets - there are more, but the main ones are Nutriment, Natures Menu and Natural Instinct. However, for large dogs like yours it might be a bit expensive. The Nutriment people are on the helpline and would be able to advise. You wouldn't lose anything by giving one of them a trial for a couple of weeks or more.
As for home cooked - yes, it is a good option IMHO, as long as you get the proportions right. I cannot remember exactly what they are but there is loads of information on the Internet. Off the top of my head, I would imagine it is something like 50 to 60% meat or fish, 20% vegetables and 20% carbohydrate although you could adjust things to suit. Of the carbs, my understanding is that sweet potato is a good one to go for although I know that David speaks well of brown rice and oats as long as they are very well cooked (until stodgy).
The dust mite is a real headache and I almost feel like saying that maybe he would be better housed (for at least part of the day) outside in a covered kennel and run. However, that is a bit extreme and he could well be more distressed especially as he is used to being in the house. It does sound as if you have all bases covered with regards to trying to eliminate the little blighters.
I have to say that I am so sorry to hear of your predicament. It must be uncomfortable for your dog and very difficult for you to see him so unhappy. Also, the expense must be crippling. I do hope that a raw diet might help. If you try the Nutriment do not be worried - it is exactly like feeding a tin of dog food. No handling of the meat - just spoon it into the weighing scales and feed.