These are quite strong distorsions indeed. You are using GRE-EPI volumes, I guess that you didn’t acquire SE-EPI volumes with AP and PA phase encoding directions? In fact, topup(from FSL), which is used for SDC in fmriprep (by calling SDCFlow) relies on the assumption that the images are SE-EPI images. GRE-EPI have similar distorsions as SE-EPI images, but they also get dropout in addition which is not helping.
If you don’t get better results with SYN, you may try SynBOLD-DISCO, for which there were some attempts to combine with fmriprep processing: Using synthetic field map from synbold-disco with fmriprep - #2 by jsein