What do I need to do to get at the springs that control how quickly the door opens?
You will have to pull the unit forward.
With luck the unit is installed in such a way that you will not have to disconnect anything.
How far back do I have to get to reach where the spring hooks? Can I slide the unit out just 6" or so, or does it have to come all the way out?
Here is the install sheet, see page 14.
https://www.whirlpool.com/digitalassets/MLPDF/Installation%20Instructions%20-%208269550.pdf