1) I don't worry about hitting target temp. I dough in ~ 140F on all my batches and heat to temp. Then start my mash timer when I hit my mash temp. Then mashout at 170 for 10-15 minutes.
2) Have you calibrated your brewmometers (kettle and mash tun)? I have the 5 gallon system and usually set my PID to 2.1-2.2F higher than my desired mash temp. That yields a mashtun brewmometer reading right at my desired mash temp. With such a small volume I'd expect my temp delta between mash and PID to be much higher than your larger system given its much higher thermal mass. There is likely something else going on if you have a 10F temp delta.
What has been your most recent mash efficiency? Im usually in the low 70s on big batches and mid-high 70s on normal gravity batches (1.050 or thereabouts).
Jeremy
1). My OCD worries about what those beta amylose are doing until I reach my desired mash temp. I'm in therapy and taking meds
2) I have a 20g gas system but do 10g batches so my thermal mass is not what it would be if I were doing 20g batches. I have not calibrated my brewmometer but have compared them with pid reading as well as other pen thermometers and they match. I accept this is not definitive proof but at least I'm honest.