Mate, I'm in Australia, just came back from a Telstra store. They had a pair of S5 and Gear 2 on display for everyone to play. So I went into Samsung App store on the S5 and downloaded the latest version of Gear Manager (being on Telstra network, it should have brought the Australian version of it). The app version was 2.0.14041404 and it was dated Apr 18th, which seems to be identical to the latest listed here. I've already tried this one in the past and it didn't work with my One M8, throwing "Parsing Error" after trying to connect it to my Gear 2 Neo. So I doubt it would cure your troubles, but you're welcome to give it a go (if you haven't done that already).
I was also interested to see how the overall experience of Gear 2 looks like on proper Sammy devices compared to what I've already seen on my One M8. After installing the Gear Manager on the S5, I reset the Gear 2 and connected them afresh. The additional software installation was handled silently (no pop-ups), unlike the way it was done on my One M8. After the connection was accomplished, I spotted 2 additional tabs in the Gear Manager (S-Health and Samsung Apps). Under S Health, you can set up the way steps/HR/sleep info is synched with S-Health app on the phone. Under Samsung Apps, you can download additional apps to the Gear.
The most interesting was to see the differences under Notifications settings. There are 3 sections for different kinds of notifications there on my One M8:
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