I don't listen to Shostakovich and never have. I 'm not familiar with the other fellow you mention either. Sorry that the humor was lost on you. I think you are defining its parameters a bit too rigidly.
I hadn't considered modality to be a strong goal here, so my feedback lacked that element. If you are going for the simple modality of folk music, that often uses a burdon to establish it, then certainly. But even modal music started using leading tones and chromatic motion as it got more complex, pretty soon. (Take a look at any 16-17th century italian harpsichord music for example)
Really good work here! I love the theme the opens the work, and it's subsequent development. Maybe it's me, but I think you should have reprised the beginning theme one last time towards the end.
I agree with MonaracheonAan that the 1st cello part should be in tenor clef during those high parts. As for the bowings, I think players can come up with whatever they are comfortable with on their own (as demonstrated in the wonderful live recording)
It's a catchy little melody, sounds well orchestrated enough. I think it can be developed a little more, perhaps a B section, and then a grander variation of the theme again.
Also I'm gonna move this to the incidental/soundtrack thread.