
As he is very submissive I would NOT get him neutered. OTT submission is often a sign of nerves - my own collie pup is the same around dogs and it's definitely nerves with her. With boys, being entire can give them more confidence via the testosterone so neutering can do the opposite, making a mild issue or even a non-issue into a major problem. I've seen it enough times to be extremely wary - a friend of mine had her husky/mal PTS last year after several years of trying overcome the devastating effects of being neutered. He went from cautious to extremely stressed and nervous and very aggressive. I'm not having my girl neutered until she's at least 2yrs old (fully physically and mentally mature) for the same reason, as a similar thing can happen in bitches and when she is ready physically and mentally, I will be reassessing based on how she's doing behaviourally.
Meantime, work on his confidence: keep meetings with other dogs extremely short, seconds at a time, moving him on and keeping it happy before he gets a chance to go all appeasey as it is very self-feeding - the more he appeases the more other dogs will respond to it, some negatively (it is annoying for the dog being appeased when it's very OTT), and that will make him want to try and appease them more. So short and sweet, and reward anything calm and confident - I have been rewarding Willow simply for staying on her feet near other dogs, and moving her away when she starts her uberwiggles or trying to flop or grin (grinning is appeasement also).
With people - if he is going very submissive and trying to flop on his back, try not to let them stroke him - it means they'll be leaning over which is scary for a dog, but more so for an appeasey and/or nervous one. Same as with dogs - short and sweet, and reward for calm and confident. If people are very insistent, tell them to crouch down so they aren't as threatening (and I do mean tell! If they won't, walk away).