Because the .243 is a "short neck" caliber I'd recommend sizing the neck all the way. You should be able to accomplish this with minimal case sizing out of a FL die or you can purchase a neck die. Even though you may be getting suitable neck tension with only a partial neck size you may have issues with excessive bullet runout not sizing the neck completely.
Yes you can use your FL die. Personally I like to size the entire neck and I like to just slightly bump the shoulder. I seem to get my most accurate loads that way.
Normally what I do is run the brass through the decapping only die. Then I trim all my brass at once(if needed). Then I normally allow my brass to tumble for the night. Then I apply a touch of Imperial sizing wax and size the brass(without the expander ball in the die), and slightly bump the shoulder back. Then I run the brass for the last time through the Sinclair neck sizing mandrel(with just a touch of Imperial). Then I tumble the brass for a final cleaning. I know this is pretty picky, and takes three strokes of the press, but it completely eliminated my run out problems.
The easy way to tell how far to adjust your die down is to take a candle and smoke the whole upper half of your case. Then run it up into your die. Wherever it sizes the smoke will be disturbed. Keep adjusting your die until you attain the desired level of sizing. Tom.