Is there currently a way to search for a sermon by (keyword in) title?
Eg add a text filter on the title field in the main sermon filtering view?

..or some way of having a cut-down version of the search that only searches sermons and not other articles etc..?

Assuming you are using the Bible Study search plug-in, the site search will search everything including Bible Studies. This URL:

www.emmanuelecc.org/index.php/search/ecc...p;limit=20&areas[0]=biblestudies

is what my web site does when searching only Bible Studies fopr "ecclesiastes". Expect you can find out for your site what the URL will be and attach that to a link or build a custom module with that HTML in it? The key bit is "areas[o]=biblestudies" ...

There may be a neater way of limiting search in Joomla - have you tried the Joomla forums?