I suppose it's possible that the streaming links have changed (I was concerned that NESN jumped into NESN360 with both feet). Anyway, maybe @tmm1 can give more guidance, perhaps instructing one of us to stream from a desktop browser and do a HAR capture for further diagnosis. I'm outside my home area right now, so can't do it myself 
(edit to add):
If someone can go to Watch - NESN.com on their desktop and try to stream the NESN feed. I was able to briefly stream the NESN+ feed in a browser and it seems to suffer from the same interspersion of incorrect content within the feed. I can't get NESN to play at all.
(edit to the edit):
@tmm1, et al., I fudged a connection and looked at the transport streams on the NESN site. It seems like they may be working. The URLs for the transport streams are https://nesnhddai.akamaized.net/hls/live/2097241/nesnhddai/.... for NESN and https://nesnplus.akamaized.net/hls/live/2094122/nesnplusprod01/... for NESN+. Not sure if this differs from what you have in Channels (or if this helps at all).