I think most aggression in dogs is fear based in one way or another, and its a bit like a piece f string if and how much it can be cured , in many cases its down to management.
Owning a DA dog , I can give you a little insight to my world, I think for a start you have to decide if you are the right home for this girl, (given your job) I have no doubt your commitment is 100% , but you have to face the fact, you may never get her over her issues, and it will be a case of management...(as with us).
The link Mini put up is worth looking at, it may give you some things to work with.
Regarding the situation you described, her laying down and you not being able to move her..which then escalates the situation.
Something I would try, it may give you a little more control if this happens again, is to buy a headcollar and a double ended lead (halti do a good one) get her used to the head collar first obviously, then when walking her, you can attach the lead to her normal collar
and the headcollar, this will give you a little more leverage when you see something coming, you will be able to bring the headcollar into force (along with her collar) to distract her away from the other dog....i.e turning her away and walking the other way, stopping her dropping to the ground, along with being able to get her to focus on you instead of the other dog.
You need to ask yourself , are you prepared for the long haul with her, this means years of managing her behaviour, you may be able to resolve her behaviour , BUT you may not, so you have to be aware off all outcomes.
My girl is 10 in a few weeks, she has mellowed over the years, we have never been able to fix her problem, we would never trust her to meet and greet another dog , we can manage her outbursts, by 1) avoiding situations, that means staying away from other dogs.......can you do that.
On the occasion she does meet other dogs, we are 100% in control, and she is never off lead.
As she has aged she is no longer as
up for it as she was when she was young, but she can still let herself down on occasion when street walking and do her thing..( scrape her feet along the ground whilst turning cartwheels) this does not happen often now, but I guess she will have the odd moment till she pops her clogs.. for the most part now, as long as dogs don't push a button, she will walk by nicely.
I am giving you an insight of what it may be like for years to come, you may resolve your situation, your girl may not have the issues mine did , or you may be a better trainer than me, but from my experience I feel these issues are more likely to stay with them, and depending on the dog it will respond differently to any rehab....
You seem committed, and I hope you can help her over her issues, but you do need to be realistic, and acknowledge , what if you cant make her better and can your lifestyle adjust to her needs.
Good luck.