LiFePO4 batteries for Wavebird controller

I came up with this idea after getting sick of my Wavebird constantly disconnecting randomly because im using 1.2v rechargeable batteries instead of standard 1.5v ones...

My idea is to use 2 LiFePO4 batteries in parallel since they're 3.2v standard, with a TP5000 charging circuit and a micro USB port fitted to the top of the controller for charging.

Would this work ok? and would I be able to charge the batteries while using the controller?