What a lovely piece. Don't understand not using vibrato on clarinet but many classical wind players don't use vibrato. And by that I don't mean just a little but absolutely no vibrato. I totally don't get it. Listen to the vibrato in the strings and get a clue.
I've talked about vibrato and the lack thereof with a lot of different folks. I think the best argument for "no vibrato" is that you're trying to go for a pure tone. However, Jim, you've nailed it with the strings: I don't think I've ever heard strings, in a performance, played with absolutely no vibrato. I'm not advocating an extremely wide vibrato, a la Lawrence Welk -- which dates me because I actually know that reference -- but even a slight one warms up the tone a lot.
I do think a lot of classical sax players could use a little less vibrato .
I teach my students to use a small vibrato on certain held notes like the dreaded C or C#. We can make inherently weak notes sound so good that way and most audience members don't even know you are employing the vibrato to fix that.