First off, it's important to note Gai did not distort space, he distorted the space. If Gai had distorted space, his body would have been ripped to shreds, a phenomenon which I would then dub the "Kamui Effect". Luckily for Gai though, he didn't do that and instead went for a quantum fluctuation, whereby he gathers energy to a single point and in this case, he twisted the energy inwards.
Now that's out of the way, we can move onto Naruto's speed. Sasuke was able to bifurcate one RG Juubidara with foot speed whilst the latter was making a conscious effort to avoid being hit. As for Shimon Gai, one RG Juubidara was able to read his movements but chose not to make much of an effort to evade so that he could fulfil his masochistic desires. As for Naruto, he was able to react to Sasuke who had teleported behind him despite the latter's efforts to distract him with a Katon, and the former even managed to move enough in time to dodge the grunt of Sasuke's attack.
