Jadeborn; but that is soooo cute! Trying to pick up things with his feet, I mean...yeah, I know he falls backwards but he is experimenting. And he will crawl (even if in a sort of modified version) but maybe for a short time, my daughter did it for three months or so only. She hated it. I know you spend a lot of time with him, some of it walking him about. Now you tell me you pick up his clues and know when he is fussing because of overtiredness, which is a very good thing (that you are so well tuned to him).
Still, nine hours wake time is a long time at his age. I do know if he wont sleep, he wont (had a niece like that, but she also used to move her leg up and down when sitting in the strolling chair in lieu of any other physical activity...she is still an hyperactive young woman nowadays). So, it will get better with age if he can handle better the "awake but calm time". One cannot be playing or physically active for 9 hours, even later in life so imagine at 6 months. He needs to entertain himself quietly, and it is no wonder that he gets bored after a time with that (since the number of quiet actitivites is limited at his age). Some children will watch the world for quite a long time, but others cannot. Besides which, he really may have teething pains.
I was sure some of the games I mentioned you know because they are pretty much universal (I,m in Spain) but I wanted to put some emphasis in quiet interaction, not tiring and interesting, at least for a while. Your other solution for those times is the stroller 45 minute walk (always less tiring than walking him about), and perhaps you could do it twice a day. I feel sure that your boy will be better in a couple of months because of two things: he seems to be sleeping less than he needs but they need less with time, so that will be better adjusted and he will be better prepared for play time with words (their blablabla) and his own body, and will tire less. At the moment, it does not seem like he is going to stay (whether sitting or lying down) quietly looking around for 20 minutes awake rest.... unless it is "in movement". Patience and good luck to you.