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2) One of the people I was forwarded to even tried to tell me coax was faster then Ethernet.
3) They told me the ont I had couldn't do Ethernet and I would have to get a new one installed and I would be billed.
4) They also told me I wouldn't be able to get video to my stb's if I used Ethernet.
1) Absolutely possible.
2) Technically true, but irrelevant. MOCA 1.0 can do 135 Mbps vs 100 Mbps for cat5 to the Actiontec. Regardless of what tier you have, you will constrained by the provisioned speed, not the connection from the ONT.
3) Nonsesne. All ONTs support Ethernet connections. Alcatel 610 and 611 ONTs do not support MOCA. Here's a link to a list of various ONTs VZ uses and what they support: http://www.dslreports.com/faq/16637
4) Not true if the Actiontec is primary. It makes NO difference to the Actiontec if it's connection to the ONT is coax or cat5. Can be true IF you replace the Actiontec with your own router AND do not create a MOCA bridge for the ONTs. The following FAQ discusses various router configurations and the various trade-offs: http://www.dslreports.com/faq/16077
When you are using the 3' cable are you disconnecting the rest of the coax network? I suspect your problem might be ingress.. disconnect all coax cable that are not connected to any thing else, and then make sure all of your connections are tight.