Lets think through this together. you already listed the most applicable rules 4.4A
bold was my addition)
An extra player (EP) is optional, but if used, it must be made known prior to
the start of the game and be listed in the line-up card in the regular batting
order.
If the EP is used, the EP must be used the entire game. If an EP is used and not listed on the line-up card the following occurs
rest doesn't apply)
4.4C
When an EP is used,
all 11 on the starting line-up must bat and any 10 of
those 11 may play defense.
Looks to me like these two state once you start the game with 11 you have to stick with 11 in the lineup! True some have thought about shorthanded rules and things, but I believe the intent of this queston was to make sure umpires knew that once you designate an EP at the start of the game they (or a substitute for them) has to hit the entire game. You can't start with an EP then get to the 4th inning and say "Bubba you been hittin like sh*t, sit down. Blue we aren't gonna do that EP thing anymore." Then in the 6th when Bubba been cryin, the coach says "All right baby Bubba go hit. Blue we want to do that EP thing again." That would be going from 11 down to 10 then back to 11, and is not allowed.
I think another intent of the question is to show some difference between the EP rule and the DP/Flex, where in the DP/Flex you can go from 10 to 9 and back again as many times as you have available subs.