I have added serial printed comments to the various loops to see how many times they run. I see 14-25 runs of the main void loop before the timers on the sensors run their time and produce new values, resulting in the distances being printed. Each run of the void loop, the "communicate ()" function runs. But it never connects.
So I'm not sure if this means anything, but at about a 14 to 25 to one ratio, the loop with the ethernet communication runs, compared to the timers for the sonic sensors producing new values and serial printing it.
Even if I could serial print the data to another device that handles the web communications, that would be good. Perhaps even a good strategy? A second arduino purely for a web server?