Mike, I'll reply to a couple of your initial questions ... it's never a good idea to puts tablets/pucks directly in the skimmer. If you have to use them, place in a floater or in-line skimmer. As Joel mentioned, the older tabs should still be good if they were stored in a cool/dry place.
Now our philosophy seems to differ a bit from there. You mentioned your readings are "spot-on", but haven't shown them yet, and that you do have a test kit. It would be good to share with us what your test levels are at the moment and what test kit you are using because it tell us if there might be any disparities in the levels. A prime example is what you are experiencing - not showing any FC (chlorine). Which one FC or CC? From there, what is your current CYA level as that determines what your FC level should be. For a pool store to give the impression that any pool can be maintained by a pre-set schedule of chemicals confirms why here at TFP we don't hold pool store testing or advice in the highest regard. Pools are a bit like pets - each is unique and needs specific attention each day.
We'd be happy to help with your chemistry if you would like. I suspect some of your levels may be in question even though you appear to be on a set schedule. If you would like our help, just let us know. Have a nice day.