I had initially tried 3dbucket. However, the resultant NIFTI file (after applying 3dAFNItoNIFTI) was not readable by Broccoli:

The exact form of the call to Broccoli was:

# Combining Subject-level nifti files using 3dBucket
[ -f volumes.nii ] && rm volumes*
3dbucket -aglueto volumes sub_1.nii.gz sub_2.nii.gz  \
                sub_3.nii.gz  \
                sub_4.nii.gz  \
                sub_5.nii.gz  \
                sub_6.nii.gz  \
                sub_7.nii.gz  \
                sub_8.nii.gz  \
                sub_9.nii.gz  \
                sub_10.nii.gz
3dAFNItoNIFTI -overwrite volumes+tlrc
rm volumes+tlrc*
3dinfo -label volumes.nii

# Run Broccoli
RandomiseGroupLevel volumes.nii -mask TT_N27_3mm_mask.nii -design design_broccoli.mat -contrasts contrast_broccoli.con -teststatistics 0 -permutations 500 -output test_broccoli

With thiis, the permutation tests by broccoli yielded the following response:

Input data is a single volume, nothing to permute!

An alternative approach for creating a nifti file that Broccoli can read is *3dTcat*. I didn't realize it initially that 3dTcat appends new volumes to the beginning of the sample volume. So creating the appropriate sample volume requires adding subject-volumes in reverse order to the rows in the design matrix.

# Combining Subject-level nifti files using 3dTcat
CNT=0
[ -f volumes.nii ] && rm volumes*
3dcopy sub_10.nii.gz volumes
3dTcat sub_9.nii.gz   -glueto     volumes+tlrc
3dTcat sub_8.nii.gz   -glueto     volumes+tlrc
3dTcat sub_7.nii.gz   -glueto     volumes+tlrc
3dTcat sub_6.nii.gz   -glueto     volumes+tlrc
3dTcat sub_5.nii.gz   -glueto     volumes+tlrc
3dTcat sub_4.nii.gz   -glueto     volumes+tlrc
3dTcat sub_3.nii.gz   -glueto     volumes+tlrc
3dTcat sub_2.nii.gz   -glueto     volumes+tlrc
3dTcat sub_1.nii.gz  -glueto     volumes+tlrc

3dAFNItoNIFTI -overwrite volumes+tlrc
rm volumes+tlrc*
3dinfo -label volumes.nii

# Run Broccoli
RandomiseGroupLevel volumes.nii -mask TT_N27_3mm_mask.nii -design design_broccoli.mat -contrasts contrast_broccoli.con -teststatistics 0 -permutations 500 -output test_broccoli

That being said, Broccoli's maintainer informed me that the "Clustsim" flag on 3dttest++ can generate non-parametric null distribution, which I was previously unaware of. However, including that flag leads to a crash on my system (the error message was placed in a different post).

Thank you for your attention.