I'm trying to catch up here - sorry for the late post.
I had to listen to this on lower volume than usual because of sleeping children in the house (ironic because it's a cradle song) and thought it was fine. (There's something slightly funky at the beginning but that's already been noted.)
I can see why you don't like the piano, though. This is probably a really stupid suggestion, but have you tried playing an entire piece una corda? The sound will be different - who knows, maybe better?? Of course, finding repertoire for which that's appropriate is challenging, but there are pieces in which it's used heavily.
Thank you, Stewart. Funny about sleeping children. Yesterday my daughter wanted to take a nap half-way through the ballet she was watching (composer Valerij Gavrilin (1939-1999). Asked if she would like me to play the piano for her she said, "Yes!" so I practised one of my later pieces, by a certain living composer (I am not giving my secrets away!
and it was not Ismagilov, either!) and she was aleep in 2 minutes - and your children wake up with 19th century cradle songs!
Technically I cannot play "una corda", because I must be the only member who does not have a grand (or 1/4) piano and, as you know, on uprights all the action does is bring the hammers closer to the strings.