360alaska said:

Could you just remove the extra two pairs of wire that give you gigabit and force the router into 10/100? Would that help things?

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I've tried that myself, with no success. A gigabit port will auto-negotiate to 100mbps and the Mac won't actually have a link.
Something like this would be a simple solution as it's 10-base T only: http://ebay.com/itm/391220099957

The mac will link with it and the Verizon router should negotiate a link with it successfully.