I found the cause, in case anyone else has the same issue. These entries in the web.config were causing issues:
<staticContent>
<mimeMap fileExtension=".otf" mimeType="font/otf" />
</staticContent>
and
<rewrite>
<rules>
<rule name="RewriteASPX">
<match url="(.*)" />
<conditions logicalGrouping="MatchAll">
<add input="{REQUEST_FILENAME}" matchType="IsFile" negate="true" />
<add input="{REQUEST_FILENAME}" matchType="IsDirectory" negate="true" />
</conditions>
<action type="Rewrite" url="{R:1}" />
</rule>
</rules>
</rewrite>