I was there a couple of weeks ago and did the 6am tour; I believe that was what we had been adviced, and what I would also advice to you. If you are really good at bird voices, then the early forest birding is unsurpassed, but it lasts a while before the light really penetrates down inside the forest. On the other hand, on the river, you will have all the light from the start.
We saw lots of good birds, but because we had not really gotten any of the real mangrove specialists (it was very windy that day, so difficult to both catch movements and hear birds), we were offered to stay on for a second run of the mangroves with the next group, and did add the Panama Flycatcher on the second round.
Most if not all CR Nat Parks open at 8, so you may not even have a chance to see much inside the park before the 9 am trip if you chose that option.
When staying at Cerro Lodge, do check up on the voice of Black-and-white Owl, which can be seen catching big insects or bats by the Pool or by the light on the way to the cabins. There were some nice hummingbirds there, and I had Rose-throated Becard in one of their trees with macaws flying over.
Niels