Hi Stephen,
You don't need to go the route of disassembling, spot welding & tag-on flexing your battery for it to work properly. The tag-on flex is only for the purpose of restoring and displaying apple's overall battery health information. Following the iFixit instructions to install a new battery should restore your phone's daily battery life to the way it was when you first bought the phone (not dropping to 50% by 9am).[br]
It's possible that your new battery simply needs calibrating. Try using your phone until the battery drains completely and turns off. Then charge it to 100% and leave it plugged in for an additional 2 hours. This should teach your phone to recognize your battery's true 100%, and true 0%.
If your phone continues to drain quickly, it is likely one of two things: [br]
#1. Your replacement battery is defective.[br]
#2. Your phone has a hardware problem that is draining your battery. A micro-soldering professional can help with this.