I haven’t read all this thread, but I am a professional dog trainer and I work almost exclusively with aggressive dogs these days.
The first thing that you need to understand is that this is not a dominance issue. Even with what little information I have about your dog, if you treat this like a dominance issue then the problem may escalate very quickly. If nothing else, neither of you will enjoy your life together. Dominance in dogs is greatly misunderstood, and in fact I tend to think it is better to disregard it (no dominance problem cannot be treated directly as a behavior problem).
You asked about getting an e-collar. For about the same price you can visit a qualified veterinary behaviourist and determine whether or not your dog has a neurological or other medical problem (e.g thyroid, brain chemistry, or even simply physical pain) which cannot be resolved, or get some advice on dealing with this problem.
If your dog has a neurological or medical problem, I can only imagine the hell that it would be living in if you were to use an e-collar to try to solve it. It is already bad enough that you are using a prong collar. Can you imagine being mentally unstable or in physical pain and having someone try to “correct” this by causing you physical pain?
While I won’t claim to not use aversives at all, I very rarely use aversives when dealing with aggressive dogs. There is an adage which is mostly true - aggression begets aggression. If your dog’s behaviour problem can be solved, it can be solved without using aversives. This may seem counter-intuitive, and many would disagree, but the fact is that I (and many others) deal with truly aggressive and dangerous dogs without ever so much as a leash pop. It is effective, regardless of the choices a dog trainer might make.
Corrections are not something you can just do and hope for the best. Poorly timed, poorly placed, or excessive corrections will do more harm than good.
Alpha-rolls and scruff shakes are a relic of the past. Dogs do not physically flip another dog over and pin them down with force. An alpha-roll is performed solely by the dog who is submitting, of their own accord. Scruff shakes are mostly seen where a dog is frightened and trying to frighten another dog, they do not assert any real or lasting authority. If they cause anything, it is avoidance and fear. This is not the same as submission or obedience (even if Cesar Millan seems to think so).
If you attempt either of these on a dog who is willing to bite you, you will get bitten sooner rather than later. Use common sense.
Don’t waste your money or time. See a veterinary behaviourist who can make a proper assessment, which includes a medical assessment. Don’t buy an e-collar, don’t see a dog trainer, don’t see a self-proclaimed animal behaviorist (I would send you to a veterinary behaviorist if you came to me), and forget about alpha-rolls or anything like that.
There are many, many factors. “Idiopathic rage syndrome” is very rare, and it usually diagnosed simply because a reason for the aggression could not be found (not because there is no reason). A good veterinary behaviourist is most likely to find a reason, behavioural or medical.
My guess would be that there is a medical reason for this behaviour. Whether or not you can afford to treat it (or even find it) is a separate issue, but please don’t force your dog to endure needless physical or psychological corrections for a condition that will probably not respond favourably to such treatment. Find out, get a qualified opinion, then if you have to put your dog down at least you will know the FACTS and will know that you did it for the right reasons.
And if you are forced to ask for advice on-line, might I suggest a dog training forum? This is a pretty serious matter and you will get a better percentage of qualified responses from a dog training or animal behaviour forum.