You may be interested in the Refugee Interview Project (RIP). This was a massive joint programme by Harvard and the USAF the early 1950s to capitalise on the large number of Soviet Displaced Persons (DPs) who found themselves in Germany after the war.

The background to the project itself is pretty interesting. This was the first time that Harvard's Russian Research Center (RRC) and the Air Force engaged in social science in a big way and there was a lot of push-back in both organisations. Not least because RIP was big: over four years a team of approx 20 researchers conducted thousands of interviews/questionnaires and produced a mountain of reports, all at a cost of almost $1m (1954 value).

The result was impressive though: the first real look at how ordinary people lived under Stalinist rule. For decades it was one of the most useful resources for understanding the Soviet system.

The archive is available online at the above link but you may not have much luck looking for testimonies from Soviet Jews. The population interviewed was skewed towards non-Great Russians (and the more generally more anti-Communist) but it was also based on those who ended the war in Germany. For obvious reasons Jews would not have been well represented in this cohort. Nonetheless, attitudes towards Jews are well captured in the interviews.