On that same trip from over 10 years ago, I also visited Beppu, and I made this "mistake" out of ignorance. I started in Hakata, went South to Kurume and the from Kurume I went East through the middle of Kyushu to get to Beppu. I didn't know that this would be the slow and scenic route that goes through quite a bit of mountainous territory. Also, the train I was riding was diesel powered unlike the mostly electric trains I was riding before, and it stopped running late at night in the middle of rural Kyushu, and I had to find a business hotel to spend the night at in a tiny town of called Hita. The scenery was really pretty, but it took a long time to get from Hakata to Beppu this way.
I found out later that it would've been way faster to take the train that goes along the East coast of Kyushu to go from Hakata to Beppu.
https://www.cityheaven.net/oita/ (VPN may be required outside of Japan)