I found that building two wells into the same cistern (A few tiles apart, the cistern is deep and wide) solved this problem: Neither of them were bucket full, whilst if there's only one well, I get "bucket full" all the time.
Unfortunately this has not worked for me. Did you make the new one closer to the main area dwarves would come from?
Oh. Sorry my method doesn't work for you.
The first time I did it it was entirely unintentional: The wells were by design in different rooms, one with a deep natural wall shaft from two levels above, the other only one level above the water. I was just trying to have wells available in different areas, one for hospital, the other for a bed/diningroom complex, and figured I could use the same cistern if there was absolutely no way dorfs would try to climb from one level to the other. For some reason, the second well got "forgotten" to be built for about six months or more, and when it was built, suddenly the "bucket full" tag was gone for good on Well #1.
Since then I've almost always put two or three wells into the same cistern, usually from different levels. It's just convenient to only have to flush one cistern, instead of three. Plus less cisterns to dig... So perhaps it's because they're often on more than one level above the water? Or perhaps because they are always in different seperate rooms, not right next to each other? Or perhaps Urist McFillbucketandleaveit gets confused and doesn't know which well to go and prank first? Your guess is as good as mine...
I keep a small bucket-only stockpile (6 buckets total) a short distance from each of my wells (perhaps two or three tiles away). That could be a factor as well, I guess. It's because otherwise, there are buckets scattered messily around the well, which annoys me... But perhaps they are using those buckets to haul away the water?