I'm in a somewhat similar situation in a game I'm playing currently, only I have a slight technological edge. (Destroyers v. Frigates, Infantry v. Rifleman, anyone?) I could probably win the space race with ease, but that's no fun being this far ahead - so why not conquer another continent and go for a domination or conquest win?
If you see a city which has most of the enemies ships in it, attack it, and do so using the Sirian Doctrine, if you can. (Stripping it of defenses with ships, then launching artillery against it and then infantry to take it directly from the ships) Once you destroy the land troops in it and take the city the navy is destroyed, and with a significant portion of his navy out of the war, he'll either have to devote valuable production to making ships, instead of land troops, or give you free reign to reinforce your armies. Either way, you win. Additionally, in my game, I have a Great Artist and several City Defender infantry ready, so that the turn after I take it the territory will be mine - with the enemy rushing to retake that, then my other invasion force will land on the other side.
If you have a GA, take it along and used it to establish a good beachhead once you take a city. And be sure to take a couple city defenders to defend your new conquest against the inevitable backlash.
That's my advice, anyway.