I've noticed this, too (I'm also on Verizon; the bf is on ATT and doesn't seem to experience this issue...)
I think that it has something to do with uploaded tracks vs. matched tracks and how the software handles retrieving the data. What I think is happening is that your data connection can get caught up trying to contact Apple servers to download/stream "uploaded" (non-matched) tracks: when a track doesn't immediately begin playing, if you've noticed, the software generally skips ahead to a song that WILL stream. I have found that after a while, music stops loading altogether and that I have to force-restart the phone (home+lock button). When it boots back up, I get notifications that "xyz song + x number of others" were not able to be downloaded.
Just an idea - I have no technical knowledge of how Apple has actually coded the service. I don't think it relates entirely to signal strength, though, because often times I find my phone streaming reliably on 1x data, but when I have 3-4 bars of LTE the streaming stutters.
Hopefully the 8.4.1 update helps with this problem