Sleep in a Muong stilt house at ban Khanh and raft the river on bamboo
Trek in, stay two nights
Book through the park rather than a Hanoi agency, and go for two nights rather than one. Treat the bamboo rafting as the reason to be there in the afternoon rather than a bolt-on. You trek in, so pack light, and the wet season makes the trail heavy going. This is also the realistic way to combine Cuc Phuong with the longer treks toward Ngoc Son and Pu Luong.