Well, GP farms are usually high on food, low on production, as you said, which makes them harder for GP birth through Wonders. Therefore, cities strong on food should go by the specialist approach.
That doesn't mean you can't go through Wonders. In fact, being Industrious + having access to Stone or Marble really *BEGS* for Wonder building, but you should opt to do so in a production intensive city, otherwise you will risk not completing the Wonders in time, losing precious time and the benefits of the Wonder to your opponents.
My suggestion is to have multiple GP farms -- if the city is focused on production, build Wonders to increase your GP output and, if possible, boost it a bit more with one or two specialists (as long as it doesn't compromise the city due to food shortages). In cities focused on food, you can use the more "traditional" approach: the specialists. Another good thing about this is that you can use each city to produce its own type of GP and have a good output of different GP types(something a single city can't do).
This strategy does bring its share of disadvantages: although very effective in the early game, the increase in the GP cost makes this tactic somewhat obsolete as time goes by. When using it, I try to adopt Pacifism as fast as possible, plus construct Wonders that increase the GP birth (ie The Parthenon). In a later stage of the game, I then switch to Free Religion (extra research), and go for one of the victory types -- the one that suits the situation the best (but hardly ever military, I confess it's not my greatest skill

) -- usually from there I go for Diplomatic, Domination (if I had expanded well from the beginning), Cultural (good tactic with Wonders, if well planned from early on, although usually harder to achieve) and, of course, my favourite: Space Race.
Sorry if my opinion is counter-productive -- I'm new to the Civ community and have still got MUCH to learn...