I am a retired social worker. I think this is a really tough call for you, and I think Hackneylass and 64 make good points as have others.
I'm a bit confused about the timeline. Was the child removed from birthmother when he was 4? If a child is not going to be able to be re-united with the birthfamily, then the LA have to formulate a care plan for the child's future. Do you know what the care plan was at that time. If not, it is something you could ask. Was he placed with his present foster carers at aged 4 (and on what basis - I imagine short term fostering) but again I think you should check. Has he been with the same foster carer for 3 years, or have there been changes of foster carers - another thing to check.
You need to know what is his legal status - the LA probably have a Care Order on him granted by the Court, but again you need to check.
My guess is that this child was placed on a short term basis (as all children are initially) and that the LA have been trying to find adopters for him for sometime, without success. Given that he is already getting help from CAMHS demonstrates that he has a lot of emotional and behavioural problems. All children of course in this situation will be affected to a greater or lesser extent, but for this child, it seems he is adversely affected, as 7 is quite young for a child to be referred to CAMHS in my experience. Also the fact that the current foster carer is calling time on the placement is another worry, and you need to find out what that is all about. It may be for all sorts of reasons of course and related to the family circumstances rather than the child, but you need to know.
To be honest you probably are this child's "last chance" because he is certainly not going to be matched with adopters, given his age and his difficulties. Sadly there is a real shortage of permanent foster carers for children of this age. SO I can see why the social worker is hoping that you will care for this child.
You said earlier on the LA want adoption, and then you mentioned Special Guardianship (I don't know what a schedule 4 assessment is) I have been retired since 2009. The thing is with either of these "routes to permanency" it means, as Hackneylass has pointed out that you are the ones literally left "holding the baby" without any support from Children's Services. LAs like adoptions and SGOs because they can close the case as the child is no longer "on the books" and it's over to you, lock, stock and barrel.
I don't think you should begin any assessment until you are fully aware of all the background details, and then you need to be clear on what basis the child should be placed with you, if you decide to go ahead. I know you are concerned about your 2 year old, and I think this is a real problem, because the 7 year old will be functioning emotionally much younger than his chronological age (as Hackneylass found out with hers) and he will have so many needs that he shouldn't have to compete with a much younger child. Good practice means that children who are experiencing emotional and behavioural problems should be the youngest child in the family.
I'm not clear if you know this child or have ever seen him, though I think you must have done as your DH says he feels "numb" (sorry if I have that wrong) but has changed his mind. I think that is a real worry to be honest. There is no doubt that this child is in dire need of permanence and stability but whether you think you can take this on needs very careful consideration.
You see you hold all the cards at the moment (though social workers won't le on...) because the only way that a child can be adopted or be subject to an SGO is if the applicants are prepared to make an application for either of these 2 Orders. The social workers might not explain that to you, well I'm pretty sure they won't because they want this child placed. I'm not suggesting that they don't want to act in the child's best interests but as someone else said it is you who will be left to deal with the difficulties that arise.
My advice is to get far more information - all documentation should be made available to you and I also think you should have the opportunity to talk to the current foster carers, and don't let the social worker try to prevent this happening. IF after careful consideration you do decide to go ahead, I think you should tell the LA that you are only prepared to go ahead on the basis of Kinship Foster Care (this means that the LA will still have Parental Responsibility for the child) and you should get the support you need, and you will be entitled to a fostering allowance for him as this is mandatory with foster care, but is discretional with adoption and SGOs. I don't know what your financial situation is, but it's an important point. The social workers won't like this because the child will still be an open case, but I think it is the "safest" route for you, and they won't turn you down, because they have no other placement for him. Fostering Regulations allow them to place the child with you after doing an initial assessment, for a period of 6 weeks before carrying out a more comprehensive assessment and getting you before the LA Fostering Panel for approval. However in reality it is often far longer than 6 weeks (can be 6 months, or longer....) before a full assessment is carried out on you.
I know the fact that I am saying there is unlikely to be another placement for him (other than another short term foster carer) is going to put pressure on you, but I think you need to know the reality. I would urge you to try not to let your heart over-rule your head. There is your DH's wish for another child, which won't happen if you take this little boy. Rolling the tape on............if this child causes a big disruption in your family (and I suspect he may well) is your DH going to resent him - and then what's going to happen. I'm sorry to be pessimistic but I have seen marriages break up and people suffer mental health problems in these situations, and birth children and fostered children suffer in the midst of it all.
Happy to help further if necessary