Welcome to Chiff and Fipple, Mmartindent.
Someone around here might be able to give advice, but in the event that there isn't, I might have a little advice.
First, it may actually be possible that you can have a chance to try them out. My experience is primarily with flute, but in my experience, flute/piccolo-vendors do mail out flutes for people to try and to return. I've also met flute-vendors who have events for individuals to come and try a range of flutes. Your best choices in this regard are to either (1) identify the
Yamaha dealer for your regionand inquire about testing a piccolo; (2), if you have a teacher, get their input regarding who in the area deals in flutes; (3) or, if you don't have a teacher, contact a flute instructor at a local university and ask them regarding your questions as well as vendors. In my experience, all three of these options have been very useful. ---Even if you can't try the specific piccolos you are asking about, it would be worthwhile to try some piccolos to get a better feel for the differences in material. See more below...
Second, Yamaha has three levels of piccolo; student, professional, and handcrafted; the 62 is in the professional category, and the 82 is in the handcrafted category. The main advertising difference between 62 and 82 is that the 82 is "handcrafted". I don't know what the difference is in practical terms for Yamaha: anything more from me in this regard is guessing. However, I would guess that they would be very similar in quality.
Regarding headjoints, again, I think this is an area where you'll want to try piccolos for yourself. The material for the headjoint is also going to affect other elements of playing than just tone, such as attack. I don't know what your current experience is with regards to flutes and piccolos, but it would be worthwhile to try the two different types of headjoints before committing to one. The tone is also pretty dependent on the player. I can expand on that if you'd like.
It seems worthwhile to mention that flutes (and presumably piccolos) differ by instrument, by this I mean if you try a piccolo and you like it, it is best to buy that piccolo. However, if you do try piccolos and then end up buying a used one of the same model, it will probably work out OK.
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Caveat: I haven't played piccolo but I played a silver-plated flute at a hobbyist level for several years. Now, I primarily play Irish Traditional Music now on a simple-system flute made of Delrin. However, I am trying to advise based off of what I gleaned from the flute-teachers I have had over the years, my own experience, and what I have learned from
Flute-Talk Magazine and the articles regarding instrument-buying advice.