I had the opportunity to call on a short old gym floor that used a division line and a parallel line on both sides of the division line at about 10 ft. off of the division line.
I had received a couple of explanations as to how to use this system and was wondering what the resident experts thought?
My thought was that when team A is bringing the ball from BC to FC, they would cross all three lines to give them the full length of a normal BC and as soon as the crossed the third line, they could back up to the third line behind them to give them a full FC...
I was told that this was incorrect..

The way I've done it in these kind of gyms. Front court is origionally established by the division line. Once front court control is established the "over and back" line is the farther of the 3 lines from Team A's basket.

I don't think this is addressed in any official rule book, so do it the way it's done in your area. If you don't know, pick what seems right to you.
Personally, I'd have a short BC. Moving from BC to FC, the first line crossed ends the 10 second count and is also the BC line for violation purposes.

This makes the most sense. Once the player crosses the 10-second line, she instantly has space behind her before committing a BC violation.

The 10-second line should be near 40 feet from B's endline, and the BC violation line should be near 40 feet from A's endline.

My experience is same as Snaqwells on this. I think this is also the easiest to explain to the players in pre-game...."first line you come to.....".

Man, does this bring back the memories of both playing and working games on this type of floor.

I agree with ref18. Makes more sense and it spaces things out.