This is the flip side of the "dogs should be allowed to play with other dogs" debate. For this dog, other dogs are a source of great excitement and excitement is a type of stress. As a result, you're starting to see him view other dogs as a source of stress also.
The tips you've got are great ones and I would use that long lead all the time, just for now. It's not a step backwards - it's bridge to take your great puppy into being a great adult, over the treacherous waters of adolescence 
Keep your distance from other dogs at all times, just for now. You want to help him re-evaluate them as a lot more boring than he currently views them.
On long leads in open spaces this probably means keeping him the other side of the field etc and using your treats to keep him moving with you rather than focussed on the other dogs.
On pavements, this means keeping enough of a distance from other dogs that you know for sure he will not bark or lunge or react You do not want him practising this behaviour - the more chances he has to practise it, the more likely he is to grow into a reactive adult. Again, use your treats to keep his focus on you and turn around go back the way you came if that's the only way to avoid coming so close to the other dog. Try and keep it low key and relaxed, if you can.
He will mature and change again and the protections you put in place now will help him do so without developing a serious behavioural issue.
With the crying, ignore it. Don't tell him to be quiet etc because any time you do, he gets some attention. It's a pita but if he never, ever gets anything he wants when he is crying then he will stop it. Dogs only ever do what works 
. Counter it with making sure he does get what he wants when he is quiet. e.g. sat in a pub, he sits down, give him a small treat straight away, then another, then wait a few seconds and another, then a few more seconds and tell him he's a good boy, then a minute and some fuss, then two and a treat, then three. You get the idea. Anytime you notice him quiet and calm (even at home) then give him a little gentle fuss and praise
Re loose lead, at 10 months old with two difference homes already it's probably not surprising he's still a bit hit and miss. I would just double check your training method is sound (there are a few different ones) and perservere. If you're not sure of your method let us know and we'll tell you what worked for us. Battendog was a bit useless on the lead until about 18 months or so - which also corresponded with outside world distractions slowly becoming less exciting.
fwiw bringing a trainer in now to help you would also be a great idea (rather than wait). You're not neurotic at all and any trainer worth their salt would much, much rather work with a dog who is still young and so doesn't have ingrained bad habits yet then wait another 6 months by which time barking at other dogs has become something much more serious because these things have a tendancy to escalate unless properly addressed quickly.