It needs be said:
1) The OP is asking about a 6hp Briggs. (that means, he's got a four stroke engine.)
2) The OP informed of his measures to attempt a fix, they failed, and they sought further "information?" - Not, how to act in front of male mechanics?
3) The OP's engine (unless someone went through painstaking retrofitting of a different carburetor) does not have a two-stage adjustable fuel mixture system. More than likely, there's NO adjustments at all for fuel-air, and only one external adjustment for the idle speed?
4) I know and agree with the ethics of this site, but the above is too much to let unsuspecting, gullible people absorb only to make their lives more hectic. Hence, on the matter of sharpening blades? You ABSOLUTELY DO NOT, make a lawnmower blade to where it'll cut you?
Take the dullest knife you can find in your kitchen drawer. Sling it around at 3600 rpm, and see how dull it is?
But more importantly, understand, when you sharpen a blade "down" to razor-edge sharpness, the only thing you're doing is assuring the very second you start hitting the grass, you'll be chipping away at that nice sharp edge, and it'll be worse than it was prior to sharpening it before you get 100 feet into the yard?
I KNOW, my wife and I have been sharpening people's and our own, for decades. Sharpening them in such a way, is simply a mockery of the design of these rotary style mowers/blades. Also understand, on a rotary engine mower, the outer 1/4"-1" does, 99 percent of the cutting of grass. If you bring that outer edge down to where it'll cut you, you'll assure your blades will be un-sharpenable and shaped like a carrot by the third time around.
5) Unbeknownst to the average joe-shmo lawnmower consumer, being "educated" on filters, off-season maintenance, location of and checking of minor components, is in fact, the job of the seller. China-mart has turned that into a joke as well. But even if their people in the garden centers are untrained and complete imbeciles on these issues, it's the consumers' responsibility to bring that to the store managers attention - because it IS, part of their contract with the manufacturers. Mechanics and service centers will take time to help some people, but it has nothing to do with whether or not they where a bra or need to.
6) So, having started, ran and sold two lawn and garden service centers over the course of a life time, being repeatedly certified by every major and many minor manufacturer(s), I feel comfortable in proclaiming, the above response is pure silliness, and the ancient "lie" of, "draining the fuel" that's been sold to consumers for decades, is absolutely, a money-making hoax to literally stir up business, and believe me, it's been the best money-making scandal we ever un-wanting-ly, innocently took part in.
But I'll end responding to this hoax, I've been round-n-round with the younger mechanics who, either haven't learned enough yet, or, knowingly assist the lies' propagation because without it, they can't generate enough money to survive. The latter is simply greed and laziness.
The ONLY time this would be good, is if, the consumer ALSO, fogged the intake and engine internal components, and indeed, some consumers do this, but it wouldn't reach 1 percent of consumer lawnmower users who would even know how, much less take the time to do so.
Therefore, the SECOND and easiest off-season habit to get into is, keeping the tank as full as it can be, (2 or 4 stroke) and then, setting down the nintendo controller long enough to go outside, start each piece of equipment every month, run it long enough to flush a carburetors'-worth of volume of gas through it, then, cap off the tank to the top again.
Finally, some footnotes on mysterious behaviors and mechanical jokes.
Most mechanics who work in a flat-rate shop, would "disallow" anyone wasting their time during work hours. You're taking cash out of their family's budget, get out of their shop, and don't be surprised if, after one or two excursions of wasting their time, you get the boot with a stern warning, boobs or no boobs.
Consider this. . . If, throughout the year, (or since whenever the system was taken completely apart, and cleaned out) - that, by the time the end of the year arrives, and you decide to "drain" the system by running it dry, what's going to happen to every drop of water, bad fuel, and foreign particulates etc., that have accumulated up in any one or more of a dozen places inside the fuel system?
That's right, it'll be forced to be sucked right up into the carb and engine - just like watching the last ounce of water scurry down a drainpipe.
NO! NO! NO! Do Not Do That!