Chad,
We generally work on escapes first. That gives them the ability to roll from the beginning. The premise for this method is, if you can't catch 'em and position on 'em than you can't submit them. We also stress a lot of conditioning to support this type of game.
I totally understand what you are thinking when you mention holding position. I often have to fight that mental fight, especially if I am rolling with someone evenly matched or a better than me. If I get position I don't want to give it up for anything.

I really want to make sure I have something before I do move. The problem with that type of game is I'll never grow. I can stall all day, to improve my game I need to try and make something happen. At least for me, that was my reason behind a cautious ground game. Fear of getting "caught". Now I just roll, of course I look for position so I can set up a sub, but I stress a lot less about getting caught. One real benefit to playing this way is I'm finding all kinds of weird ways to make subs work. I talked with Luis Gutierrez about this and he shared the same thoughts. Its hard to describe in print, but try this to start. Next time you roll, don't go for any subs. Just see how many times you can change positions. As you move around your opponent take note of how many things open up. It will amaze you. It did me, I couldn't believe how many things I was missing by just holding position.
Its a different game, but give it a whirl, if you don't like it, discard it.
Speaking of new guys..., this is the perfect game to play with them. They are just learning escapes and positioning. When you roll with them they can work escapes and you can work constant pressure through positional changes. You probably won't have to worry about getting caught in a sub since they are new and don't have any yet. You will both benefit, you work changes and set ups, they can work escapes into position.
I dig the comment about stick in hand. As they say around here, thats how you get off the bottom of a pile!
Peace,
Paul Sharp
http://www.championjiujitsu.com