How to remove kitchen faucet

It's a single-hole unit by Kohler. The problem is that the nut that screws in from under the sink to secure the faucet is round (2-1/4 inches diameter), not six-sided. So there is nothing for a pair of vise-grips or a channel-lock wrench to grab onto even though the nut is rather thick, maybe 1/8".
It has two threaded holes for screws that dig into the bottom of the counter to keep the nut from loosening. I've loosened the screws, and tried using them to get leverage to loosen the nut. No luck.
I don't know if a basin wrench will work on a round nut.
I sprayed with a lubricant, but the real problem is that I can't get a good grip on the nut.
Eleven years ago, most likely I installed the faucet onto the new sink before I placed the sink into the counter cutout, so everything was more accessible. I'm trying to avoid removing the sink, but that's my last resort if nobody has some other suggestions.
Kohler sucks, for using a round nut. If they hadn't used cheap plastic, the handle wouldn't have broken and I wouldn't be going through this ordeal. On the other hand, I've used it for 11 years, and it was in used by the previous owner for an unknown number of years. He and I are both single, so the faucet doesn't get the heavy use that it would with a family of, say, four.
TIA.
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Rebel1 wrote:

Hi, Instead lubricant, try penetrating oil. Give some time for the oil to work.
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wrote:

Bang on the nut, or the metal fixture, to get the penetrating oil to go farther in. Liiquid wrench's own instructions say to do this.
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Rebel1, 7/5/2011,11:23:43 PM, wrote:

Can you stick a screwdriver in one of those holes at the correct angle and tap the bottom of the handle with a hammer to loosen the nut?
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Sometime I overlook the obvious. The original screws were 3/4" long. I replaced them with screws 2.5" long (I just happened to have them on hand). Then I simply used by thumbs against the long screws to twist the nut off. It really wasn't very tight. (Maybe the lubricant I sprayed helped, too.
Maybe I could have used thumb pressure against the original screws, but I thought the longer screws would give me more space.
Thanks Tony and Bad Golfer for your comments.
R1
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It's great when something so simple turns out to work so well!!!
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