This is a good thread for newer brewers who might gain insight without having to repeat the shortcomings we have all gone through from time to time.
Craftmeister alkaline is the boss for cleaning and you can use it in repeated applications (I have a keg washer made out of a 6 gallon bucket with a submersible pump and rod with holes drilled into it to spray the inside of the keg or other vessel - I love it for my Kegmenter, too. I tend to rinse things to remove initial deposits of crud and let them accumulate in number for series cleaning of multiple vessels in one night). If you have some really stiff beerstone, the dairy product from the Farm & Fleet or equivalent is great as a soak (something like 3 ozs in 5 gallons soaked for a few days will literally allow wiping off the beerstone). I had no luck with Barkeepers' Friend on beer stone - it is oxalic acid, but did not help for me in getting the oxalate off, even with a paste and significant scrubbing. I love it however in getting the bottom of the stainless boil kettle and the SS electric elements to shine. White or blue scrubbies or the dobie are what I use for wiping off sticky crud (never any steel wool or stainless scrubbies for the reasons stated).
I have heard that acid followed by alkaline or vice versa really clears off the beerstone quickly, so if time is a factor, those could be used in short succession, perhaps (I like to soak in the dairy product to allow the phosphoric to do its trick over a few days).