How do I deal with or avoid a full map?
If all the cities on the map have been filled in (35 cities in 5 regions), then SOMEONE will have built 14 cities and so the game ends -- 13 cities each for 6 players is only 78 of the 105 available places.

Its not necessary for a player to be able to power all 14 cities -- they just have to build them to trigger the end of the game.  The player who powers the most cities at the end of that turn (even if it is less than 14) wins.