Basically much of what you said there is accurate but I'll clarify some stuff.
The thing that makes Run for MKII Kung Lao and Jax good is they don't change from a walking animation into a running animation, like MK1 Kano and MK1 Raiden, so it's similar to Smoke's run and throw in MKII.
The Supermonk move is definitely a great spot on punisher as you said, and you can even connect it sometimes after an air Dive Kick close to the ground.
The Dive Kick works the same but hits differently (different collision itself) than MK3 Kung Lao's. Also, JK, Dive air count is 31% vs 24% for MK3 Kung Lao.
The Spin is definitely not as good as MK3 Kung Lao's, but not entirely useless. It is however disabled after any hit, and does not push back in the corner, but you can't move around like MK3 Kung Lao can in MKT.
I would say his RH is in the running for best ever. Liu's is amazing but Kung's, I dunno, I think it could be even better.
His uppercut whiffs similar to MK3 Kung Lao's.
He has the option for sweeps and comboing his autocombos, including his pop up, even though it's blockable, it's pretty useful.
His overall damage is higher, in the MKII damage bracket, and his chip damage is ridiculous as well.
He has lots of fun high damage combos that require some level of effort, and the fact that he can pop you up and start the semi infinite to me puts him nearly at the level of Rain and Noob Saibot. As Iori said you have significant options with him even when you screw up. I love this character.