getting more from batteries via series connection
Your calculation for the series case is incorrect.  You forgot that since the batteries are in series, you can only use the 2 Ah of each cell.  100 W / 7.4 V = 13.5 A.  2 Ah / 13.5 A = 9 minutes, just like your answer for the parallel case.  You can't cheat conservation of energy.

Also, calculating battery runtime to better than 1 part in 500 (one second out of 8 minutes 53 seconds) is absurd.  Battery capacity is a rough number at some set of nominal conditions.  Various factors, like temperature, drain rate (current), age, what you consider "empty", number of charge/recharge cycles for rechargables, and part to part variation change the total charge you will get from the battery.  Take a look at a battery datasheet.  Batteries are complicated.