I feel like I've found the equivalent of a cheat code. If you sort of stutter step via a rapid series of mini swipes (like when trying to both run from AND attack an enemy), you can manufacture a much higher attack speed than you have per your stats, especially at earlier levels, because the end of each little swipe will be an attack regardless of your current attack speed. Hopefully that makes sense! It can get exhausting if you do that the entire run though... Also, I've now collected all relics (whale, mug, and whatever the third one is) by spamming the 5th (last) run of the first set/chapter. I assume will be necessary for the next one.