Have you got a link to the post on Reddit? I didn't notice it on there, I'd be interested to see the responses
You might struggle to get a private lesson that early in the morning. A lot of gyms advertise privates lessons 'after 10am' once the morning session has finished. You might be able to arrange something earlier, though.
A few people on here have trained at Attachai, so they'd know better. But looking at the map you'd get the BTS to On Nut, then get a taxi from On Nut Road to the gym. Or you might possibly be able to get a motorbike taxi to take you down the smaller alleys.
Yokkao is pretty close to Asok. The gym gets mixed reviews, but I'm sure privates would be good as they've got some excellent trainers there. Sylvie has a session with Singdam in the library which is really good.
Eminent Air gets very good reviews. You could take the BTS to Punnawithi station, it's not too far from there.
As for me, I've had a few private lessons with Sagat when he was at TBM, which were really good. He's at 13 Coins now.
I've trained with both Hippy and Kasemlek at Hippy's gym, which was excellent. It's worth going to Hippy's gym just to meet Hippy, he's a little character and the sweetest guy you could ever meet. Great trainer as well. He was away when I was in Bangkok again earlier this year, but he arranged for me to train with Kasemlek which was great. Brilliant trainer and a top bloke.
Also had a couple of private lessons at Jaroenthong's branch on Phra Athit as it was right next to where I usually stay. I forget the trainers name now, but he was very good, I enjoyed working with him. Edit: Had a look on their website and found him, his name's Pongpat
Also had one private at a place called JW Muay Thai, as google maps said it was open on a Sunday (most gyms are usually closed). I got there and it was closed, but a trainer came down and gave me a private lesson anyway, which was very nice of him. Just had a look and the gym's closed now.