One thing I recently realized I messed up in my first couple of games was the number of mountain strips that are supposed to be in play at the start of the game, so you might try double-checking that.
Yes, there should be two mountains available in 1-3 player games and 3 in 4 player games. Note that the latter means there will not be a new mountain added at the end of round 6 in a 4 player game. Otherwise you have been playing correctly. Not that it is not necessarily efficient to hoard a lot of resources, so on the long run you might exhaust the strips less.
Relatedly, also remember that you can buy ships with silver outright, making using wood for them less critical.