CYA *will* sit on your filter for a few days, but it won't clog it.
Liquid CYA is based on the sodium salt of cyanuric acid you mentioned. A cheaper and easier way to add CYA is simply to chlorinate with dichlor granules for the first few weeks. For each ppm of chlorine you add that way, you also add almost a ppm of CYA! As long as you NEED cyanuric acid, this is a very good deal, both in terms of price and convenience.
If you have access to a Sams Club, their PoolBrand undiluted dichlor (50# bucket; 24# box) is usually the best deal going. But I'll post links to Amazon, in case you can't use Sams Club. Most other stores -- Costco, Walmart, Kmart, etc -- sell diluted dichlor.
To use dichlor, just add doses to the skimmer, with the pump running. With 13K gallons, a reasonable dose would be 1 pound (about 2 cups) in the skimmer each evening. Each dose will add about 5 ppm chlorine and 4 ppm of stabilizer. Once you have added (5) doses, you'll have enough CYA in the pool to have an effect.
Have you ordered a K2006 test kit, yet? Regardless, get a cheap OTO/phenol red kit, and adjust your dose the following evening, based on pH and chlorine levels.
Regarding your filter, apparently Water Way made two models of that filter, and you have to match replacements by length.
Here are the Amazon dichlor links:
PoolBrand granular dichlor 50lbs @ Sams Club => ~$2.20/lb (May 2014 in Chattanooga)
PoolBrand dichlor bagged shock 24lbs @ Sams Club => ~$2.50/lb (May 2014 in Chattanooga)
Kem-Tek dichlor 22 lbs @ Amazon => ~$3.50/lb (May 2014)
Kem-Tek dichlor 12 lbs @ Amazon => ~$4.10/lb (May 2014)
Kem-Tek dichlor 5 lbs @ Amazon => ~$5.00/lb (May 2014)
Kem-Tek dichlor 2 lbs @ Amazon => ~$9.00/lb (May 2014)
Keep in mind that Amazon products normally ship free; and that in many parts of the country, you will not have to pay sales tax. Shipping + tax can increase the cost from other suppliers by 15 - 40%, so compare delivered cost, not nominal price.
KemTek brand products may also be available at local Home Depots; match pictures here to what you see at Home Depot, before you buy. Otherwise you may end up with diluted dichlor there, too.
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