I believe there are some differences in how an ambient temperature probe and a meat probe behave. (Happy to be educated to just how wrong I am
I'd trust the built-in probe. Unless it's just absolutely caked up dirty I wouldn't bother cleaning it. If I couldn't touch the dirty and have it fall off then it's not dirty enough for me to care.
Otherwise, for my purposes 15 degrees is just 'noise' and it would have to be some fringe case for it to matter in the slightest. When I ran the analog #2 I had temperature swings of +/- 40 degrees and it never mattered once.
I hope this comes across reassuring and not as dismissive. Your questions are totally valid.