The continuous batting order does have a rule stated in 4.04 that players who arrive late are placed at the end of the lineup. The last sentence in 4.04 is "Also, if a child arrives late to a game site, if the manager chooses to enter him/her in the lineup (see Rule 4.01 Note) he would be entered into the lineup at the end of the current lineup."
I do not believe that a league should mandate something that is already spelled out in the rulebook. Especially if it contradicts with the rule as written.
The batting order is the players listed in the lineup handed to the umpire to start a game. As an umpire in a game resumed with a continuous lineup I would not allow a team to insert new players batting immediately unless they were at the end of the lineup and that position was due up to bat.
I would disagree that there is no "last" batter in a continuous batting order once a game begins. The lineup is static unless new players are added to the end of the lineup. Or a player who leaves the game for injury or other reason, in which that position is skipped when it is due up (Note 2 in 4.04)