Tony,
I think the shortcoming of this solution may be the voltage and discharge current rate. Your battery pack will probably provide similar power to the original NiMh pack, which means you will be limited to the middle power setting (i.e. not 5w).?
I have a Windcamp battery in mine, which stays just above 11v for multiple 1h activations, and it permits full power output. It is worth noting that when you are below 12v the power icon will blink at 5w: this is normal. I read somewhere that 11.4v is what the ft-817 likes to run most efficiently, which is why the Windcamp pack is set for that voltage area. I have no idea if there is any truth in this.
So, if you were to add two more cells to your pack, you would get better performance. But you will still be limited by the current draw rate of those cells which are probably not designed to output much current. I have seen a lot of people use 3x 18650 cells, which kind of fit in the battery bay. Or the Windcamp setup is very tidy and works well. With 18650s you can buy a regulator from ebay or amazon for a 3 cell setup, which allows you to charge them from any 12v source... And the batteries can be bought new or taken from old tools or laptops. Usually a battery pack fails because one cell falls out of line, leaving the others in good shape.
73.
Tobias KK7BCO/2M0TFF