Yes frustrating isn't it ?
I also had this problem when using the EE Dac with a Teralink X (Mk1 version) USB to SPDIF converter.
I believe the reason is the Sabre DAC in the EE Dac wont lock onto a higher jitter source effectively, this has been shown to be the case with the Buffalo Sabre Dac too.
Your EE Dac will however work perfectly from a Hi-Face. I dont know if it will work with the other converters you've mention.
Hope this is some help