Trying for culture victory. Help! Hopeless?

Sweden, 5 cities. 2 Campus, 2 Amphitheaters, Great Library. Have only met 2 other civs. Suzerain of the science CS that give +1 GP points for districts.

It's turn 200. Already won 2 Great Scientists but no GWs yet. I was trying for a quick culture win. Bust?

Even if so I will keep going as I have 3 Natural Wonders to myself - Old Faithful, oasis one and the Iceland volcano. It's going to be very easy to get a TS in all terrains.