(I posted this after Mark. It's a different perspective, mostly because I'm concerned that initially with no CYA you may get to near-zero chlorine levels and allow algae to grow. This might be overly conservative since the chlorine level will build up overnight and even the small amount of CYA in the first few days will be better than nothing at all.)
You can go as low as you want, but the lower the CYA level the faster the chlorine usage from breakdown by the UV in sunlight. So for uncovered pools exposed to lots of sunlight, I wouldn't go any lower than 20 ppm and even then you'll likely use 60% or more of your FC in one day. With 30 ppm, you may lose more like 50% in a day. The tablets only dissolve at a fixed rate, though that is somewhat adjustable via the openings in the floating feeder or by the number of tablets you use. So this means that you need to have the openings and number of tablets higher when the CYA level is lower in order to keep up. As the CYA level rises over time, you should be able to reduce the opening size or number of tablets in the feeder.
If there is any way to get water dilution, be it from rain overflow, backwashing, or intentional dilution, then that's the best way to keep CYA in check in which case higher CYA levels can be used. Nevertheless, the amount of dilution needed is still pretty substantial so I can understand why you want to take the approach of starting out with low CYA.
I would not use Trichlor tablets in the skimmer unless they are designed to not dissolve with no water flow (most are not) as they are too acidic.
The problem with no CYA in the water isn't the FC/CYA ratio, but rather the FC getting used up faster than the Trichlor tabs can keep up, but perhaps with enough in a floater at full throttle, maybe it will be OK.