I've been searching for a way to run a shortcode from a widget; WP doesn't normally process shortcodes in widgets, but passes it through as text.
I installed Enhanced Text Widget today for other uses, but on a whim inserted a short code. Lo and behold, it worked! I'm pretty sure it's Enhanced Text Widget that did the trick because it didn't work before.
You helped me solve two problems in one. So, thank you.