Looking this over I can see several ways the Apple family could have handled things better:
1. Get some help. While the four Apple family members may do just fine for running things most of the year, things like Cider Season or Applebuck Season look like they need extra hooves to get things done in a timely manner. Even if they can't afford hired help for some reason or Applejack doesn't want to keep using her friends then I'm sure they could get Berry Punch or some pony to help out and just pay her in barrels of cider or something (Dang, that idea sounds slightly horrible for some reason).
2. Do the applebucking beforehand. Unless their cider requires squeezing the apples withing 10 minutes of their being picked then it would make sense to harvest the apples, sort them, and then press them all in one go instead of running the whole process at the same time. I'm not sure if the rules of their competition would have prevented the Apple family from bucking and sorting apples all evening and then having a stockpile to press during the competition but that could have helped speed them up for the one hour they competed.
3. Like lordofchange said, stockpile barrels for a week or so and sell them to the town. Or heck, just sell it by the barrel and not have the whole town stand in a huge line to drink mugs of cider at a little lemonade stand. If apple magic requires it to be drunk out of those wooden mugs then just sell the mugs along with the barrels. Or bottle it or whatever.
4. When the FlimFlam brothers showed up then the Apples need somepony skilled in negotiating deals. I suppose its because I'm a huge fan of Fallout Equestria but I keep thinking there is a "Barter" skill and Big Macintosh has that tagged. I think its because Lauran Faust once mentioned that originally Big Macintosh was supposed to own Sweet Apple Acres while Applejack handled the day to day stuff. Too bad Big Mac is a silent protagonist.
5. Even if the Apple family secret recipe for cider requires them to work slowly, there's no reason they couldn't have the FlimFlam brothers use the machine to make barrels of their stuff alongside it. Like, they have a small amount of Original Apple Family Cider which they sell for X bits and a larger amount of FlimFlam Cider which they can sell for cheaper. That way they can sell both ciders alongside eachother and even with the current (stupid) setup then someone like Pinkie Pie could grab a whole bunch of both cider at the start of the line, Berry Punch could get a lot of the cheaper stuff, and Rainbow Dash at the end is guaranteed at least a little bit of Original Apple Family Cider or she can get the FlimFlam stuff.
Other thoughts:
That machine is pretty cool. I doubt that the FlimFlam brothers have magic as powerful as Twilights (even combined) but they seem pretty good at incorporating their magic with technology, using it to control the machine. Make it drive around, control the apple harvesting funnel, and power it. It releases smoke so its probably uses some kind of fuel along with magic (unless the smoke is from it processing apples and all its power is really from unicorn magic).
In Applebuck season, Twilight was able to harvest apples from a whole mess of trees and people wondered if unicorns had an advantage over Earth Ponies when it comes to farming, looks like these unicorns got the idea. They may not be able to levitate a whole fields worth of apples like Twilight but their machine lets them do it just as well. They may not even have the alleged earth pony ability to grow plants but they sure can harvest them (and I'm guessing they can sell them thanks to their song and dance routine). Its pretty clear that they aren't members of the extended Apple family clan so these twins must have gotten their apple marks more as a result of them personally having an interest in apples and less on being members of a family whos business involves apples.
Also, according to Wikipedia the word "Nonpareil" is french for "without equal" and is also the name for little
colored sprinkles. My personal headcanon is that when Pinkie heard the brothers call themselves "Traveling Salesponies Nonpareil", she was confused because she suddenly thought of little colored sprinkles used to decorate cupcakes.
Fry: No! They did it! They blew it up! And then the apes blew up their society too. How could this happen? And then the birds took over and ruined their society. And then the cows. And then... I don't know, is that a slug, maybe? Noooo!
Futurama: The Late Philip J. Fry