Actually the $2.99 HarborFreight meter is probably working just fine. The ohm measuring point in a two wire measurement system is inside the meter. The range switch may induce some "unexplained" resistance hooking the ohm current source to the voltage test jack but it really doesn't matter because you WILL have lead resistance anyway.
Slowly rotate the range switch, click, click, click, about 3 full turns (SLOWLY) to clean internal contacts that have been sitting unused for the past 3 years. Plug the test leads in just like you have them, them unplug, them re-plug, etc. to clean the test jack. Turn the meter on and touch the two probe tips together and hold (you have the meter set up just fine in the photo) until the reading stabilizes, or ALMOST stabilizes. This is the "2 wire resistance" of your test setup. The HarborFreight test leads have a surprisingly high resistance just by themselves.
Subtract this from your atty resistance measurement.
Rocket