I've visited the Belum state park this August, and stayed at the Banding Lakeside Inn. No problem, because I rented a car.
Be careful with the Pulau Banding Jetty, because it's a bit far away from the east-west road (where the bus would likely drop you off). No problem if you have somebody from the Belum Eco Resort who picks you up with a car and brings you from the main road to the jetty.
If not, it can be a challenge to roll a suitcase with wheels on that not so smooth road full of holes (especially under strong sun or if it rains).
Regarding the taxi option, I met a couple in Ulu Muda who paid RM 250 from transportation from Pinang (Georgetown) to the Muda lake. That's 150km. If you found a taxi driver from Kota Bharu willing to bring you from Belum to Kota Bharu for RM 300 or less, that would sound like a good deal.
Do a Google search for "Kota Bharu taxi" - that might be the solution.