The main reason Trichlor pucks/tabs are so popular is that they are the only reliable slow-dissolving form of chlorine. There are also Cal-Hypo tabs, but they require more fillers to bind them together and tend to fall apart as they get smaller. Unfortunately, there is no slow-dissolving tablet form of chlorine that does not have the side effect of increasing CYA, as with Trichlor, or CH as with Cal-Hypo. There is also Dichlor, but that's only in powdered form and increases CYA even faster than Trichlor for the same chlorine amount. That's just the way the chemistry works.
There is a solid form of chlorine, lithium hypochlorite, that doesn't have these side effects, but it only comes in powdered form and it is very expensive.
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In my case the added CH wouldn't hurt but I still think the clear winner is plain ol' chlorine injection. After awhile w/ hypochlor tabs I think you'd get a CH build up - much like the CYA build up from trichlor.
As an aside, I did notice today that there is a tap in the bottom side of my tab chlorinator that I think would be an ideal place for my injector/ck valve. Not sure if they all have that but it might be worth a look. Beats the c/rap outta doing extra plumbing.