1-3 is a problem
Unless you are following a strict Wonging regimen, a spread of 1-3 isn't enough for six-deck play. 1-3 would probably generate a small profit in the double-deck game, but not a lot. You could use an exit strategy on the six-decker and get by with a 1-4 spread, but unless you are getting great penetration, the six-decker you described isn't a very good game. The two-decker is passable, and if it has good penetration, it could be a very acceptable game.
I don't know of a general rule for a "session" bankroll. Each person's definition of what a "session" is can vary. I like to bring 10 max bets with me when I go to a casino for a one-shot hit, but everyone has his own idea about what is good. It is better to simply approach the game as one long session with breaks for food, sleep, work, family life, etc.