Strange that the Gear Manager on the Play Store says not supported, since its only requirement is a device sporting an Android version of 4.3 (Jelly Bean) and higher. Which Android version are you running on that S4?
Also, you're using the Samsung Gear app, not the Gear 360 app? If you downloaded it from APKMirror, did you download the app called Gear S Plugin? That's the name of the Gear app once it's installed.
Tasker has a Mic Mute action, and TaskS2 lets you start Tasker actions from the watch (but read the comments in the Samsung store; maybe the people complaining there just need to exclude TaskS2 from doze mode, maybe it's worse).
If you're into soccer ball, then Goal+ kinda works. Almost. I installed it last night as a companion to the Android app. It showed me all the Champions League fixtures and usually shows me the live results too.
I say usually, because last night the Live Results didn't update. :(
Searching amazon for "gear s2 band" found a few. Shouldn't matter if it's 3G or non-3G, band connects are the same.
https://www.amazon.com/Samsung-Milanese-Magnetic-Stainless-Connector/dp/B01I9V86VQ/
That looks like it even comes with normal adapters, I suspect the connect adapters are compatible with 20mm bands, a la gear s2 classic.