Rambuchan
The Funky President
Very promising project. Well done so far 
Your lack of naval warfare is simply fixed. Make all the ships much much cheaper on the build cost. Cheap ships = AI going for naval warfare. There is more you can do on this front but try it and see if your first Punic War happens.
You can also even out the tech research rates with judicious placement of river tiles (little ones here and there) and certain resources or luxuries which boost trade. So, for example, plonk a few more of these in Britain and you boost their research rate and also growth, which of course equals more science. But focus on the trade boosting resources/luxuries first as the growth could get out of hand. The good thing about this technique is you can bring certain civs in line without imbalancing everything else. These are just fine tuning tech tips. To deal with the 'thousand years out if whack' go with Quinzy's tips.

Your lack of naval warfare is simply fixed. Make all the ships much much cheaper on the build cost. Cheap ships = AI going for naval warfare. There is more you can do on this front but try it and see if your first Punic War happens.
You can also even out the tech research rates with judicious placement of river tiles (little ones here and there) and certain resources or luxuries which boost trade. So, for example, plonk a few more of these in Britain and you boost their research rate and also growth, which of course equals more science. But focus on the trade boosting resources/luxuries first as the growth could get out of hand. The good thing about this technique is you can bring certain civs in line without imbalancing everything else. These are just fine tuning tech tips. To deal with the 'thousand years out if whack' go with Quinzy's tips.