There are some issues with these calculations.
1) The per pound price:
- The prices you used are per kilogram, not per pound
- The prices do not take into account the first stage reusability that will presumably become standard by the time the sats are launched
- If we use the Falcon Heavy costs with reusability (e.g. from here) we get $50mil/(0.7*119930) = about $600 per pound.
- The $600 price per pound includes the SpaceX profit margin. If that is not taken into account the price would be even lower.
2) SpaceX will first launch only 1600 sats to make the system operational. From then on the future expansion can be funded by the operational profits.
Given the above calculations, the launch prices for getting the system to work will be 1600*850*600 = $816 million
That is well within the SpaceX financial capabilities.
Now, the above assumes that the FH launches of the sats would be mass limited, rather than volume limited. I suspect that in reality they would be volume limited, however, thus the price would be higher. In any case it would be much lower than your original estimate.