David, welcome to the forum!
You're quite right to mistrust those "unsearched" lots on
ebay. Given the hype of most, I find it highly unlikely that they have not been searched.
To answer your question of where to find truly unsearched lots of coins, I don't have any good answer except to suggest you hang around your favorite coin shop, make friends with the owner, and hope if he comes into any large numbers of unsearched coins which he doesn't want to sort, he'll call on you. I suspect this would be more applicable to cents rather than anything else.
One of our members, Kyra (Rachael) works in a bank and is in a position to cherry-pick large numbers of coins, but most of us are not normally exposed to these numbers. For accumulations of unsearched older coins (say, a friend's father just died with several cigar boxes of unsorted coins), I think it might be a matter of being in the right place at the right time.
That said, I have appraised a number of friends' cigar box accumulations with the intent to provide the owners with the collections' values rather than looking for hole-fillers in my own collection, but the opportunity was there. Most of these contacts were through local organizations to which I belonged, e.g., ham radio club, Boy Scouts. Once it is known that you are a serious coin collectors, those with lots of unsorted coins will come to you.