I use Onyx, so I am not entirely familiar with your setup, but we run the FC 9000 and I pretty much only use the segmented area correction - this is different than the multiple marks. If I start a job for segmented area correction, it will scan the first 4 marks across the sheet, then the next 2 marks that correspond to the end of the first segment (the first "side 'T" marks"), then it cuts the first segment, scans the next set of marks, makes a correction, cuts the second segment, and repeats until the end of the image.
What you described about it scanning all the marks first, this happens to me when I use the multiple marks option in Onyx - and it does not do a segment area correction. I think it adjusts for the entire image as if it is static, but when cutting the rollers can slip a little (very tiny slips here), making it necessary to correct while cutting. The segmented area correction correct every segment and has nice results.
Lastly, when our Graphtec scans marks correctly, but will not cut, it usually means something is too close to the image or to the edge of the sheet - by something I mean the rollers, or the head (well, image too close to the edge will place the head too close to the edge....) for some reason the Graphtec will not cut very close to the outside rollers' paths.