Hi
A couple of points.
Using a wireless remote or self timer automatically disables the SR so that should not be an issue.
People unfortunately move around so 1/30th of a second may be a bit slow in my opinion.
Depth of field. Check your Dof with this handy calculator
http://www.dofmaster.com/dofjs.html .
My estimation of DoF using figures you supply are 3.34 feet at f5.6 and 4.4 feet at f7.1. This assumes you were focusing on the correct point at 6 feet. Using multipoint Autofocus, it is a bit hard to be sure where the camera decided to focus. If the camera focused on the lady in front in both cases you acceptable DoF behind her is only 2.1 feet an 2.9 feet respectively. This may not be enough in a group shot where people are behind one another.
Did you focus before activating the remote? 1/2 press shutter button or Rear AF button. Using the remote does
NOT activate the autofocus mechanism (K-7 and K-5-IIs) unless using Remote Control 0-RC1 and pressing the correct button.
Cover the optical view finder as light entering the camera here can affect exposure.