Z93 is at least 5800 years old. It is much older than CWC. Z93 was already in Kazakhstan before any Sintashta or Corded Ware Cultures were formed.My provisional view is that Z93 was an offshoot from most likely Southern Polish/NW Ukrainian Corded Ware that for the most part migrated eastwards across the Steppe towards the Caspian Sea on Corded Ware's demise.
Like as you said that Corded Ware was not only limited to Z283, but also I1, I2, R1b and other haplogoups. So, ancient Aryans were not only limited to Z94, but also other haplogroups that can be found in Asia.
By the time when people started to call themselves Aryans in Asia, Z93 already involved into Z94. That means that Z94 was already part of the Aryans. And Z94 (evolved from Z93) has nothing to do with 'Southern Polish/NW Ukrainian Corded War'.
CWC was not 'Aryan' since it belonged to a diffent branch of R1a than 'Aryan' Z94. Also, like you said R1a was not the only DNA in CWC. CWC had also dna like R1b, I1.
And Z94 was not the only dna in Mitanni. Mitanni were also J2a and other dna.
If Mitanni had some R1a, than it would be most likely Z94, since by that time there was already a split of Z94 from Z93. But nevertheless, autosomally speaking, Mitanni 'Aryans' from 1600 BC were very different from CWC from 2200 BC or Sintashta.
Z94 in Levite Jews has nothing to do with CWC or Sintashta, but came most likely from the Hurrians and ancient Mitanni, Persians, Medes or Parthians.