Indeed, that's the very first thing I tried to do. I checked with the big lumber yards in my area, and the smallest stock I could find in cedar was 1x2 x 16', which would still have to be ripped further, and it was a lot more expensive than the fence pickets, plus there would have been a delivery charge.
Anyway, since I changed the game plan to just cutting strips off the pickets, this is going to work out ok, and shouldn't be dangerous. It has had the added benefit of "forcing me" to buy, and learn, a new tool - the table saw - which I'm sure will come in handy for other things. Or, if I don't want to keep it, I can put it back up on Craiglist where I got it.
This morning I made the zero-clearance insert, so I'll be doing a test run, and if all goes well with that I should be able to begin.