Forget all the crap with cleaning stock 5200 flex circuits. As you've already stated, you'll notice it's a revolving door of periodic cleanings. I went thru what your experiencing now many many years ago.

Buy some Rev9 Flex Circuits and replace your old circuits with those. You will never need to do another thing with your 5200 controllers. I had my 2 stock controllers rebuilt with the Rev 9 circuits about 6 years ago, and let me tell you I play the bejesus out of my 5200, and I have not had a single problem with any buttons on either controller ever since the rebuild.

So, my advice is to pay the $25 per circuit, or whatever the going rate is these days, and save yourself alot of hassle and time, and repair those 5200 sticks of yours for good. The Gold dot pad is probably a good idea too, but I'm not familiar with that and I don't think my sticks had that upgrade.

EDIT* That rebuild kit in the ebay link you provided is Exactly what you want.