gmapping and navigation beyond range of LIDAR sensor

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I am trying to use gmapping and the navigation stack to navigate around a large mostly empty room. I have two problems:

1. When building my map free areas are only mapped between the robot and obstacles. This leaves the center of the room unmapped. Later the navigation stack tries to navigate around the completely empty center of the room. How do I map the empty space where my Lidar returns inf?
2. I'm worried that while I'm driving through the middle of the room, because I'm essentially dead reckoning, errors will propagate and I will loose a decent position estimate by amcl. Is my only solution to get a sensor with more range?

Cheers!