For a quick answer to your question as to can the correction be made simply by offsetting the tail stock, the question of how consistent is the taper, must first be answered.
You say the part is 30" long and tapers .009". Make marks with a sharpie every 1" along the parts length. .009/30=.0003 so, you should see the part grow/shrink .0003 every inch. If this is what is happening, then your machine is cutting straight, the tail stock must simply be adjusted.
If however your measurements are erratic, for instance there is no change over some areas and a larger change in other areas, then the cause is much more complex. In that case is could be caused by bed twist, wear, head stock alignment, or most likely some combination.
Either way, you really should level(align) your machine's bed anyway. Not only will it make holding tolerances easier, but will also avoid premature wear caused by misalignment. Also, it looks like your machine is of the type where the head stock can be swiveled, so head stock alignment should be checked as well as tail stock alignment.
Do some searching here, this subject has been covered many, many times. Be careful though, not all the info out there is good.