Ron,
are you trying to use some kind of weaving or circle pattern?
First try simply dragging the rod along in a straigt line. Many rods will weld very well this way, the metal core tends to burn back within the outer coating, so that your arc length is automatically controlled to a nice short distance while you drag along on the coating.
Hold the rod perpendicular to the flat positon plate, and lean the top of the rod forward about 20 degrees, and drag the weld along. To tie into the previous bead, also angle the top of the rod about 20 degrees or so away from the bead, so the arc is melting the toe of the first bead and also the unwelded base metal. Ideally, in stringer bead overlay like you show, the beads would over lap 50% or so, and the finished surface would have minimal hills and valleys.
6013 is a good, mild arc, easy to run rod on an AC buzz box.
7014 is a great rod for flat position welding, it has an extra thick coating with iron power added, and is refered to a drag type rod, because it works great this way. With the current set properly, and the right speed, the bead is very smooth and the flux with gently curl up and lift off the finished bead as you weld. Try this rod!, then try the big brother 7024.
IMO, the type of stick welding power supply is not very critical to making good welds. I guess professional pipe liners swear by the old Lincolns, but for most people, you can make good quality, attractive welds with an AC buzz box.
Regarding the older 6013 perfoming better than the new batch, possibly it has picked up some moisture in the coating that is affecting it. I've heard/read somewhere about welders dipping their rods in water, and apparently it has the effect of increasing penetration due to the gas evolved as the water dissociates in the arc?