After some more doc-diving, I discovered the problem is that if you use encode_json (which is equivalent to $json_text = JSON::XS->new->utf8->encode ($perl_scalar) AND set the file encoding to utf8, then text gets double-encoded. When I do this

open(OUT,">twitter-non-en.json") or die "Can't open output: $!";
#binmode OUT, ':encoding(UTF-8)';
print OUT encode_json($sample);
close OUT;
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The JSON contains the expected Cyrillic text. Thanks for all the input.