By "29.97 sequence" you seem to mean a 29.97p sequence, since you speak of "editing out the frames". If FCP doubled the first frame of each group of four frames this is not "bad FCP pulldown". It is an expected "nearest frame" rate conversion for 24->30. Then it is possible to do a "nearest frame" rate conversion from 30->24 to eliminate the doublings. I'd do this in Compressor where there's a semblance of control.
In Compressor you'd leave the file at 29.97 fps and make duration 80% using "Fast (Nearest frame)". (Use a low loss codec like ProRes HQ in Compressor, lest it do a recompression.) What Compressor then does is this:
leaves the first 5 frames intact;
omits the next frame;
leaves the next 4 frames intact;
omits the next frame;
leaves the next 4 frames intact;
omits the next frame;
etc.
Note the inconsistency in Compressor concerning the first frame of the input. Study the cadence in your input carefully and then add some slug frames as needed so that Compressor removes your duplicated frames. Finally conform the result to 23.976 fps. Spot check the output for lack of doubled frames.
Dennis Couzin
Berlin, Germany