Thank you so much for playing and taking the time to write this insightful post!
I see what you mean about the spider. You are clearly very skilled at the game, so it is not challenging to you, but it kind of needs to be that speed for newer players so they can get past it at all. HOWEVER, you're giving me an idea where it could speed up a lot if you get the double jump in, say, under 2 minutes (which would prove that you're speedrunning!). I'm not sure if we'll have time to add that, but I am now tempted to do so :)
Quick-restart is another thing that I don't want in the game off-the-bat since a new player accidentally clicking it would be very sad, but maybe I could bury it in a menu or cheat code somewhere... hmm
Stats summary is also a neat idea! I see why duration of a run but I'm less clear on the usefulness of single and double jump counts, could you explain why you want those?