An unjustifiably sexist comment, but who cares, I would say boys of 7 and 8 however lovely they are would make a saint yell occasionally. They are high energy, need watching to stop them from doing insane things, they still do insane things, they have huge emotions, and are generally high maintenance! So, be aware that you are not alone, and it won't last forever! I really do recommend ahaparenting, this is an article about shouting, but she also says great things about raising great kids which are inspiring and achievable (or the dream of them being achievable is sustaining..):
www.ahaparenting.com/blog/Plan_to_Stop_Yelling
(I recently had gave a party for nine 8 year olds and suffered from PTSD for a week afterwards) (And they are all great kids)
You do sound burnt out. Is it at all feasible that you go for a week's holiday on all inclusive or something or is that not possible at the moment? Though boys would be with you, having no other responsibilities will still be a relief and will take you out of your situation, and they will burn off energy swimming etc.
Long walks for you on your own if you don't already will reset things for you and give you some perspective, as in, the boys will eventually grow up and become human!!
As an adoptee from similar sort of circs I would agree with you re social workers getting involved being stressful for the boys but I would definitely, definitely talk to one of the clinical psychologists at Beaconhouse.Org.Uk or similar as they will assess and have clear insights and strategies which will really help, day to day, and they can explain how to get funding for the service.
From what I know of NATP which has been much recommended on here, it is fine for moral support but if you want to change things for you and the boys I would say go to a good clinical psychologist with experience of adoption and developmental trauma -NATP is good for moral support though. Some of the methods recommended by NATP were around when I was a child and they are fine as emergency measures but there are drawbacks to using them as the key strategies ime.
Lastly I know a couple of adopter families who are part of a local support group to them which really helps them because the adopters are their kind of adopters, so to speak, and they are in similar situations, so if you could like minded people with similar situations that it might help you a lot.