I also see issues streaming Live TV to Safari and Firefox, not so much on Chrome.
Streaming recordings are not an issue.
I assume by the channel you are streaming Live TV from Comcast with an HDHR Prime (since SDust Premium TV is dying and doesn't use that ch#) and the channel is AVC/H.264 HD since your DVR is remuxing instead of transcoding.
When you stream this with a web browser, your DVR computer will remux the live stream to convert the AC3 (Dolby) audio to AAC which a web browser can support.
So the signal comes into your HDHR Prime, gets input into your Channels DVR (Mac mini?), remuxed and written to a folder on your DVR computer in small pieces, then sent out over the network to whatever web browser client you use to view it on.
So you have network traffic from your HDHR Prime to your DVR computer, DVR computer remuxes it and re-writes it out in small chunks (~1 sec each) called HLS segments to your DVR computer hard drive and then sends those out as requested to your client browser over the network which is constantly asking your DVR computer for new chunks (segments). Lots of moving parts.
I have issues with Live TV remux and transcode for web viewing locally. Until this is solved, I'm not attempting remote web browser streaming.
P.S. Just wanted to add that sometimes you will see cable and ota broadcasts where the audio drops out (corrupted audio packets) for anywhere from a split second to many seconds and this may be the issue with the remux failing. Depending on the player it may stutter, repeat or just drop the audio and video to keep in sync.