An update: I attempted to define the spherical source as a custom source (explained here, but modified to a spherical source as explained here). Still using an Am241 sphere with a radius of 1 cm (which is also the source radius), I now get the following tallied current:
OpenMC: 0.6192793400000001
OpenMC counts in 1 MeV peak: 0.5011834100000001
which is obviously in better agreement with both Serpent and MCNP for the spherical source than when using “SphericalIndependent” to create the source. For now, I’ll stick with using the custom source method for my spherical source.