Just my personal opinion, unless it interferes with moms' work schedule, I would ask mom to deliver child both visits...the Wednesdays and Fridays. I do not know if there is some protocol around if judge feels like asking too much, if he/she will just say no....but could always backpeddle to having mom transfer specifically on the EOW Friday nights.
For that matter, I wonder if its cool in your legal motion to just frankly state your bottom line, you'd like mom to transfer daughter Friday nights.
After that point clear, go ahead and state you'd like the court to consider having mom also transfer the daughter on Wednesday evenings as well.
Perhaps include some type of request that while a change in your work schedule is not at all anticipated, for the sake of eliminating a possible court date in the future, should your Friday night schedule revert back to the earlier pickup with daughter, that it be written in the court order that child comes to you at that earlier time...same as has been until now.
Personally, I think a earlier transition would be not just better for your time with your daughter on Friday nights, but 10 is simply a late transition time for a child.