Perhaps, Yakovlev Yak-30?http://www.airwar.ru/enc/other/yak30.html
I understand, this aircraft didn't exactly fulfill your's description, at least you could tell us, that windtunnel model was NOT Yak-30.
By the way, I couldn't find the picture at this moment, but there was a student-made design (even mock-up has been build) of small jet trainer in USSR, similar to L-29. The main difference was an air intake - as far as I remember, this was a prpo for the movie...
Sorry, no additional data.
Concerning the windtunnel tests of foreign aircraft in USSR - this is interesting theme. It's obvious, that Soviet aircraft industry has had a capabilities, greater, then Chezholslovakia, Poland etc. So its possible that such cooperation exists. There was a famous photo of L-39 fuselage, attached under Tu-16' belly for (I think) real jet testing in flying condition.