Sorry to hear about Baxter's recent experiences....
I don't think, however, it's all as bad as you feel it is at the minute.

I think, as you have highlighted in your post, a major issue is you being able to control his pushy behaviour with other dogs. This could well have provoked the attack he suffered...
Do you know any dogs locally that will either ignore his pushiness, or will give him a measured "telling off" - if you were still local I would volunteer Honey for this, as she's very good at telling pushy dogs to back off...

I think it's entirely possible that the long-line is making him feel more vulnerable - we never experienced how Honey reacts to other dogs on a long-line, as we only used it for occassional specific training purposes, but on-lead (even a loose lead) she is just as you describe Baxter to be - she will approach wagging, but suddenly turn and snarl... I am just VERY picky about who I let her say hello to on lead. If a dog I'm not sure about approaches when she is on-lead and I can see she is feeling stressed, I let her off - she wil chase the dog away, but at least she is in control of the situation. I've had some filthy looks off a couple of owners when I've done this, but I just tell them she hates being approached when on-lead.
For the time-being I would try and limit his interactions with other dogs - you don't want to let him get into the habit of reacting to dogs in this way. Work on his recall (maybe try whistle training), and heelwork off lead. Another useful thing to train is a hand-target - a touch of nose onto your hand. This can be very handy for redirecting a stressed dog's attention onto you.
Try and find situations where he can socialise appropriately - so calm dogs that aren't going to allow him to psuh them around, but also aren't going to escalate his snapping into a fight. Owners who are confident with their dogs. Or, if possinble, a doggy socialisation group (that worked wonders with Honey!!!!).
Gradually build up his exposure to other dogs... walk in tandem with other dogs, so they can be alongside each other, but not close enough to cause any kind of reaction.
If he does greet a dog, call him away straight away and praise him - don't let it get to the next step of the growl and snarl... (easier said than done, I know, and there will be times he gets there first!!!). If he does react to a dog, just walk away from him - that is the best way to show him you don't like his behaviour.
In situations where he is being pushy with other dogs, you do need to be more proactive - call him away and keep him away the minute he starts pawing another dog.
Learn what works for him - Honey is much better with another dog if she has seen it in advance and had the chance to watch its body language etc... whereas for some dogs this would escalate their tension and make them more likely to react.
As far as some of your other points...
Possessiveness of items around other dogs is ENTIRELY natural - dogs are not natural sharers, and within their own territory they are going to protect their property. I would avoid having toys out when other dogs visit... and if possible I'd also lift the water bowl. If there's going to be another dog for any length of time, I'd go the other way and put down several water bowls - it's less likely to be guarded if it's not as precious!
I would just leave him be in the evenings - Honey has never been one for lots of fuss and attention, and for her evenings are definately for relaxing... she's not keen on being approached, but because we have never pushed this she will now come to us for fuss when she wants it... heading off for some space when she's had enough.
I wouldn't worry about his food either - Honey will sometimes refuse her meals (also on BARF) - dogs are designed to eat large meals and than fast for a couple of days... most dogs have been conditioned by us to expect more regular meals, but they really don't need them. As long as he isn't going several days without food, that is fine. Top Barks did recently post something about the carbohydrates being used to help dog behaviour....
(Copied and pasted from the thread Top Barks posted in:
A small carbohydrate meal after his main ration might help too.
Have a look at this
Val Strong's diet for aggression.
· Two meals of an easily digested protein source, such as lamb and rice complete food (morning and evening)
· To each of these meals add Vitamin B6 (1mg/kg dose)
· Approx 3 hours after each of these meals add a small saucer (depends on weight of dog - approx 2oz for an average Labrador) of pure carbohydrate e.g. boiled potatoes or boiled white pasta
Keep the dog on this regime for up to 3 months, during which other behavioural and training exercises should be undertaken to allow sufficient time for new responses to be fully learned.
Signs of improvement can often be seen with 7-10 days
The diet boosts serotonin levels in the brain which not only makes the dog elevates mood, but helps the dog to control impulsivity, aggressive behaviour, ADHD, anxiety and learning problems.
A lack of serotonin causes a reduction of the reward cascade, which means that new or alternative behaviours cannot be learned, and also causes an increase in touch sensitivity.
(Taken from The Dog's Dinner by Val Strong 1999 published by Alpha, UK)
I'm sure the "easily digestable protein meal" could be any BARF meal, as that is protein in its purest source!
WRT children - it sounds like he is nervous of them. Honey is similar. We have been encouraging any child who wants to say hello to Honey to give her a treat. We also fuss Honey at the same time, so she feels more secure.
I'm aware I've kind of waffled a lot in this reply, but I hope it makes some sense.
It's also worth bearing in mind he could still be in pain following his injury and this will effect his interactions with other dogs. And while the vet may have given him a clean bill of health, there could be some physical consequences from the attack - if possible I'd get him seen by a McTimoney Chiropractor, as this has helped Honey tremendously! (They aren't too expensive, and can sometimes be covered by insurance!)
If your finances can stretch, I imagine T-Touch would also be very beneficial to Baxter.