the player can accelerate themselves forward (only after double jump) without any speed cap whatsoever, it seems that your override for acceleration can interfere with a double jump

I was unable to reproduce. Horizontal movement speed acceleration (WASD) is capped to the airstrafe_max_speed config option (default 0.7 blocks/sec). Note that air friction is reduced after a double jump compared to normal minecraft physics, this is intentional (minecraft's air friction is way too large). Try setting airstrafe_max_speed to 0, and you should be unable to accelerate after a double jump.