I like to do speed-thrus -- fast as you can go, no acting.  This can be done lines only or onstage with blocking.  If they can't do it without "acting," then they are probably in a rut.

I also like to play around with different genres -- try this scene as an opera or whatever.

Or have people sit very close to each other and do the scene without worrying about it carrying beyond their scene partner -- just concentrate on connecting with each other.

And although you want to stay away from improv, I've found it helpful to improvise what happens right before a scene begins -- usually it gives people a lot of new ideas of what is going on with their characters.

Best director I ever had did this:

She whispered directions in the ears of the actors that the other actors didn't hear.  In one ill fated love scene my director whispered in my ear, "If you don't make a solid connection with her in this scene you will never see her again."

In my acting partner's ear she whispered, "If you let him touch you you will never see him again."

As we began the scene I immediately attempted to establish intimacy by touching the actress.  She ran from me!  I was mystified!  The director was thrilled!  We played it like that.  I couldn't understand why she was rebuffing my affection, it made me work all the harder to gain her affections.  It was extremely effective and I use it to this day with my actors when I am directing.

Tom

You are absolutely right - the moment before the entrance is one of the most important moments in the play.  We have all seen the actor enter and get into character after the entrance.

Make sure your actor makes what happened in the moment before important to him/her.  Describe the door:  "it is a standard brown wood door" - Boring!!!  "it looks like someone tried to break in the door with an axe" or "it is painted with strange colors that try to suck me through it" or something similar that works for the character in your play. 

How was your day so far: "ok." - Boring!!!  "The traffic was terrible - I thought I would never get here then the elevator was broken so I had to climb the stairs" or "It started to rain - I couldn't get a cab and had to walk the whole 40 blocks" are far more interesting for the actor and will be for the audience even though they never see it.  Remember Kramer's entrances in Seinfeld?  Always different and always interesting. 

My favorite moment before questions are "Why are you here?  What made you come here at this time?  What are you going to accomplish?  Where did you come from?  How did you get here? 

And my favorite of all:  Why is this day different from every other day in your life?  (If it wasn't the most important day in your life the playwright would have written about another day.)

I'm not sure what this is called but it helps.

Have your actors repeat the last line that was said as a question - then they say their own line.

here's an example (although a weak one) - the line said before is repeated as a question (in italics) then the actual line that is in the script is in bold.

TONI: Hi Billie. Come here a minute.

BILLIE: Come here a minute?    Oh, hi. OK.

TONI: Oh, Hi Ok?  Did you see the game last night?

BILLIE: Did I see the game last night? No, what game?

TONI: No, what game? You're kidding! You don't even know what game?

BILLIE: I don't even know what game? No, I don't. Why? What game was last night?
CJ: What game was last night? Even I saw last night's game.

BILLIE: Even CJ saw last night's game? I don't follow sports.

CJ: You don't follow sports?  What do you mean you don't follow sports? Everybody follows sports.

BILLIE: Everybody follows sports? I don't. So I guess not everybody follows sports.