I think I have an understanding of how Availability works. At least, I can see a system that seems compatible with what's hinted at in the book, and which makes sense. My problem is that I don't know for certain, because the core book kind of glosses over it. So, let me describe how I think Availability is supposed to work, and y'all let me know if I'm wrong.

Suppose I have 38 Fellowship, and am trained in Inquiry. I am seeking a Rare item.

If I search in a community below 1000 people, finding a Rare item is a Very Hard roll, done at -30. On an 8 or below, I find my item, and it takes me 1 hour to do so.
If I search in a community below 10,000 people, finding a Rare item is a Hard roll, done at -20. On an 18 or below, I find my item, and it takes me 1d10 hours to do so. On an 8 or below, I have one degree of success, and move up one unit of measurement so it takes me 1 hour to find it, same as if I'd rolled that 8 in a small community.
If I search in a community below 100,000 people, finding a Rare item is a Difficult roll, done at -10. On a 28 or below, I find my item, and it takes me 1d10 days to do so. On an 18 or below, I have one degree of success, move up one unit of measurement, and find the item in 1d10 hours - same as if I'd rolled that 18 in a sub-10k community. On an 8 or below, I make the roll with two degrees of success, and find the item in 1 hour, same as if I'd rolled that 8 in a sub-1000 community.
If I search in a community above 100,000 people, finding a Rare item is a Challenging roll, done at +0. On a 38 or below, I find my item, and it takes me 1d10 weeks. On a 28 or below, I have one degree of success, and it takes me 1d10 days to find the item. On an 18 or below, I have two degrees of success, and it takes me 1d10 hours. On an 8 or below, I have a whopping 3 degrees of success, and find it in 1 hour. All just as though I'd rolled in the correspondingly smaller communities.

I think that's how it's supposed to work. Looking in a larger community doesn't increase the amount of time it takes to find an item, it simply widens your margins of where you can look. An 8 will get me that Rare item in 1 hour no matter where I'm looking (barring GM fiat), but looking in increasingly large communities gives me more margin of error for the search - letting me succeed on a 9-18, but upping the time to 1d10 hours, or on a 19-28, but upping the time to 1d10 days, etc. Is this right?

As far as I can tell, you've got everything right. The reason it takes longer in larger communities is because they're larger, and there is consequently more ground to cover. In a community of 1000 people, you can find everything there is to find in an hour. Not so in a teeming, bustling city.