I think you need to look at why you have flat beer? And prevent the cause not try and fix it after the fact. Bit on our operation: there are three of us that bottle on a Wednesday night, a brew each of the tinned kits, Coopers, Mangrove Jacks, Black Rock etc... We clean and bottle approx 90 long necks a night.
We had similar issues a while back, and we found two issues contributing to our problems:
1. Bottles would occasionally be flat and occasionally explode, this was due to either being missed (flat) during priming or double sugared (exploding). We moved to batch priming our wort prior to bottling. This just involves taking a measured amount of sugar and mixing with enough hot water to make a syrup/slurry, and pouring into wort just prior to bottling with a little swirl of the spoon, no need to sugar individual bottles, you can then do a combination of stubbies and long necks etc... with all bottles getting their share of the prime.
2. We were still getting the occasional flat, over the next month or two of batches this started increasing, we bottle in long necks a combination of twist and crown pop tops. After some investigating and testing we established "Warwick" our capper after 30 years of use between two different brew groups had worn on the capping head not sealing the bottle 100% this was more an issue on the twist tops than the pop tops. Our mate's old man had another capper that he no longer used we done several brews with it virtually eliminating all issues of flat beers.
Our only bottle issues since have been a couple explode, and a couple infected, we have now started out in giving all our bottles a good over haul and quarantining any that aren't cleaning up as they should, with approx 2,000 long necks in circulation between the three of us it will take a little while to get through them all with only 90 getting bottled each Wednesday night, and less now I have moved over to kegging.
Hope this helps and gives and gives you a couple of things to look at, and if you want any other pointers etc... please feel free to shout out.