For example (note: the basin is open by redstone underneath):

Notably, it works for regular source-flowing fluid blocks (water, lava)

This is caused by the raw ender constantly updating neighbors inside FlowingFluid#tick. When the basin is updated it resets the consume timer, so it never is able to consume. The issue seems to be that when the FlowingFluid is handling flow/spread, the FluidState it creates is different from the one which already exists, ie there is a discrepancy between what FlowingFluid expects and what RawEnderFluid creates.