As always....RTFM. (Read The Fn Manual) first.
That required advice now fulfilled by me....
Great machines. Yes, there's a lot of those machines that they're not using but that makes them the same as many. I've worked at (too many) other shops that also don't use the features that save time and prevent crashes. One is the "Z axis stroke check" function for setting the initial headstock position.
What you're supposed to do is run through the main spindle program once with no stock in the "air cut" mode with the "Z stroke check" engaged. That sets the variable for the Z axis start position and assures no overtravel. In theory, this works perfect. In reality, no shop I've ever worked at uses it. Ever. I also notice few people use the data management page you mentioned to setup for the one-button cutoff. Use it, it can't hurt. Older machines may not even have that feature though. Any chance those are 16i-T controls?
You absolutely should be using the M code for broken cutoff tool detection. Unless you have a well-documented tool life management system for the cutoff tool and a very short cycle time that you're trying to reduce even further, that little mechanical arm is worth it's weight in gold for saving broken tools. I often see it in disrepair, frequently missing the arm completely.
That Fanuc 16 control is good, but Star is notorious for having minimal options lit up. If you have any documentation, see if there's a listing of what options the machines have. Some machines have C axis on both spindles, some have it on neither one. You are probably already missing my favorite Citizen feature: the tool set mode. You get accustomed to running the first part of a program (up to the M20) to do a cutoff.
I can probably help with developing a standard program format for you, but what's in the Star manuals is already good and proven.