The math checks out...
A Li-Ion cell is not included with the battery pack mod kit. Below are some options and links to reputable sources for Li-Ion cells.
When purchasing ensure:
Battery Size = 18650
Nominal Voltage = 3.6V (4.2V peak)
Note, the Li-Ion cell does not need to have internal protections since the battery pack has protection circuitry built in.
The capacity of the Li-Ion cell will determine the battery life of your remote.
Use the following formula to estimate your battery life:
[Battery Capacity (mAh)] / [200mA] = [Battery Life (hrs)]
Example: a Li-Ion cell with a capacity of 2500mAh will give the remote a battery life of approximately...
[2500 mAh] / [200mA] = 12.5 hr