Should I rewrap my bars so the tape goes to the stem? Here's a pic of how they're wrapped now for reference:


If so should I wrap from the inside out using no finishing tape and the bar plugs to hold it together or out inwards like you do with drops.

And finally, tape recommendation? I'm leaning towards Cinelli gel cork which is what I have on there now and pretty comfortable; but I hear good things about the Fizik microtex tape and kinda like the look.