Hi,
An update: Adobe Muse CC 2014.1 (released earlier today) includes support for self-hosted web fonts. To use a specific font in your Muse site (such as the Avalon that you purchased from FontSpring), you will need to install the system font (properly licensed for desktop use) and provide the corresponding web font files (properly licensed for use on a website).
Give it a try and let us know if you need help or run into issues.
Thanks,
Abhishek