I use this exact thermometor for mashing. It is the tru-temp and I got it from target lol. It's got the "rounded L-shaped" probe. I've tested it to death like you have and I can also confirm that it's off by different amounts at different spots.
I only use it to measure about a 10 degree temperature range (149-158 mashing temp range). In this range it reads 2 degrees hot for me. I just know this after using it enough times. The first 10 brews I used it on I used both the tru-temp and a floating thermometer to compare till I was comforatble enough to just use the true temp.
I've used it for about 15-20 brews and still use it. I like it bc it has the probe and cord and I can keep my tun closed and still know what's going on inside without opening my lid. I just know that it's 2 degrees hot so if it says I'm mashing at 157 it's really 155 etc.''
I do use the floating thermometor for everything else (measuring strike temp, heating sparge water, etc.). The tru-temp is strictly for seeing if I hit my mash temp and monitoring the temp over the course of the mash and only because it has the probe and is convenient.
Stick your floater or other thermometer in there with it till you get a feel for it.
Up next: Kolsch, Alpha Squirrel, Tripel rebrew, Witbier
Currently Fermenting: Charlie Sheen (barleywine)
Kegged: Tiger Blood IPA, Irish Red, Strict Observance Tripel
Bottled: Dry Stout, Pliny the ..... Squirrel?, Cream Ale