A few notes about your post:
This doesn't really have a bearing on this issue, as all your clients seem to be wireless. Bandwidth doesn't seem to at issue, merely latency.
The quality of the streams is the same as the source. The only difference is that the server is taking the transport streams (TS) it uses internally, and remuxing those to HLS; the content doesn't change, only the parcel within which you receive it.
I am glad you found a solution that works for you.