It is possible to alter the sinc interpolation parameters in a couple of ways with Unix environment variables, at least in the version of 3dAllineate that I made for myself today to experiment with these things. I could compile this up for you, if you want.

However, the changes don't make much different, at least in the images I played with (1 mm resolution, interpolated to 0.5 mm grid). The things you can change are:

5 or 7 voxel radius for interpolation (5 = default)
cubical or spherical interpolation mask (cubical = default and is considerably faster)
taper start point (0.5 = default, can alter from 0 to 0.8, larger = less tapering)

None of these made much difference in the the ringing artifacts that I saw -- some, to be sure, which at least shows that the different parameters ARE having some effect.

Did you try quintic interpolation? There is a tradeoff between interpolation width/accuracy and the amount of ringing, at least with interpolation methods that are linear in the data. Nonlinear methods can preserve features such as local monotonicity, but they are harder to implement and much slower.