anyone know if ripping apart the note 3 wireless charging cover would work in the same way with a inductive charging mat?
Yes, the inductive circuit inside the note 3 charging cover should work for the S3, S4, S5, Note 2, etc. But you will need a QI compatible charging mat, not the Touchstone.
You will have to manage how to reposition the charging pins because they are different in every model (as they did in this post with the Palm circuit). Also, the Note 3 has 3 pins instead of one but the bottom one is for the wake function, so you will not need to wire this one. There are also two other pins in the Note 3 above the battery. This ones are for a NFC circuit. The Note 3 has the NFC circuit in the battery and since the wireless charging circuit is placed over the battery, this nulls the original NFC circuit. To solve this, the inductive circuit has also NFC added. I don't know for sure if the charging cover has the NFC circuit. In case it has connectors for those two pins, most sure is it has it. Many third party inductive patches don't have the NFC circuit, only the charging, so using them, the NFC function of the phone can't be used.