While digital thermometers are great, they can lead to the results you've listed above: trusting too much to the temp swings as it contacts hot or cool spots in the tun. To fix that problem either use an analog therm or do as you also suggest- wait a minute to take a reading. Personally I use an analog thermometer- because it's cheaper- and take many readings in various positions (both lateral and vertical/ depth) within the tun after dough-in.
To answer you questions:
1. Yes. In my experience the calc's are right. BeerSmith tells me to strike a cold tun at 164.5 for a 152 mash target, I do it. Only when I stray from that strike temp have I had a problem. Like so many other things in this hobby you must know your equipment. If the calc's you use always end up a degree low, be aware of it and adjust accordingly.
2. I'll again use my technique for example (because it's the only one I know...). While the thermo is in the mash, stir constantly but gently. The goal here is to evenly distribute both hot and cold spots. Check the temp in various locations and depths in the mash. I leave the thermo in the tun throughout the mash and check it 4 times: during the initial stir as described above, after leaving it set for 5-15 minutes, at the 30-45 minutes mark, and when the mash is finished.
What are your temp drops during the mash? As in, if you settle at 152, do you end at 152, or does the temp drop to 145? Those data won't help much with your strike temp problem but it may reveal any heat loss through the tun- especially since you preheat. Kyle