Beetlejuice stage door

There is really no perfect solution. That said, there is also no "on time." The people who do sign will sign for every person they can, so whether you are the first person they see when they open the stage door, or the last hanger-ons at the end, they will typically sign.

This is usually only an issue when there is a big star or somesuch in a show, and they may only sign a few things on their way to their car. For Beetlejuice, that isn't an issue. Some people may have other obligations and have to skip the line, some may be under the weather and skip it to give themselves maximum recovery time until their next performance. But nothing you can do will impact any of this. So, see the show, when the cast are leaving the stage, head out, and you're good.

The people you don't end up meeting, or don't get to sign your Playbill... will be the same ones you aren't going to get no matter when you get to the stage door.

Some people may have other obligations and have to skip the line, some may be under the weather and skip it to give themselves maximum recovery time until their next performance. 

They don't need a reason. They could feel perfectly fine and have no obligations, but still choose to not come out. 

OP,

Be respectful, have a sharpie ready, don't take up too much of their time with multiple questions, if they don't want their picture taken don't ask again, and remember that you are paying for the show. That's it. Your admission doesn't include autographs or meeting the actors after the show. Alex rarely comes out because of disrespectful fans and not feeling safe, which is understandable. Enjoy the show. 

Yeah it always depends. I sat mezzanine and left after the show, got to the very back of the line with no barricades and still got signatures. You never know who will come out. My friend has seen it five times and only saw Sophia once. When I saw it we got Dana, Kerry, and Presley