I think I mostly have this sorted out after quite a bit of experimentation and research. The "skips" do seem to be network related (mostly).
I changed my server setting to L16 @ 44.1k which helped quite a bit. My receiver can handle L24 96k but maybe my network could not. This setting change removed quite a bit of the skips. However, it was not perfect.
Next I began looking into my network settings. In the NIC properties of my media server I disabled all of the offloading options. After some research, it sounds like in most cases the CPU can handle those tasks faster than the NIC and for streaming media (again, it sounds like) speed in processing network tasks is critical. I guess in situations where the NIC is being utilized during heavy CPU tasks the offloading might be beneficial but based on my observations, playing music from JRiver over DLNA does not seem to be CPU intensive.
Next, I disabled flow control both on my NIC and on my router (a Cisco RVS4000). My research suggested that flow control causes the packets to be delayed at the network interface which is bad for streaming media. One article I read suggested that QoS can't even function on a network using flow control.
So the skips are eliminated on all but that one FLAC album I have. It's weird, if I listen to it over headphones at the computer it sounds just fine but over DLNA it has the little skip sounds. I tried converting it to ALAC (which is the format most of my library is in) but the skips remain. I can live with it. Frankly, I'm sick of that album from all my "testing".
I hope some of this stuff helps someone else. I'm not an expert and some of the decisions I've made could be wrong but it's honestly really difficult to figure out how your NIC properties should be set in any environment, let alone one that needs to stream media. I suspect if I were not using the powerline network I wouldn't have had to be so finicky in my settings.