OK...so I may need to make some adjustments to my new bars and the hi tech foam set I put on is all in the wrong place and umpy (ugh+lumpy)

Can I unwrap my leather bar tape (again) completely and then put it back on?

I was thinking I might just use a length of the Cinelli cork I took off..take it a turn around the top bar and then re wrap w/the Brooks....AFTER I get position settled.