I had great plans for this section, but I came home from Day Job at midday feeling icky, and have been asleep until a half hour ago.
In short, apart from whatever UU resources you find, get a couple of solid hymnals and prayer anthologies. If they come from more sophisticated Christian traditions, they will certainly have works of an aesthetic quality which aren't-necessarily-Christian, perhaps some Jewish works, and resources for alternate tune that might be easier to pull off than what you currently use. Worship in Song: A Friends Hymnal (Friends General Conference) isn't bad for small, tuneless congregations. (Opinions, anyone?)
Now, here's the deal. You're not necessarily going to use the hymnal for the hymns to be sung in worship. (And you ought not use the ones in copyright without permission.) You want good lines -- perhaps the declarative themes for worship. More importantly, you want the indices, especially if the hymnal has liturgical elements.
Here's a secret, especially if you have some older Episcopalian or Anglican resources: some non-descript Sundays have internal themes that can be summed up as topics. Episcopalians are better than most about producing literature that matches Sundays and other observances with devotional literature that's essentially the "non-scriptural reading" a lot of Unitarian Universalist look for, particularly in the lyrical theist end of things.
Gail Ramshaw's Treasures Old and New: Images in the Lectionary (Augsburg/Fortress, 2002; link to Powells) does a good job of this in forty "images" like city, harvest, sacrifice, and wisdom. Each has a few elements, and an interpretive essay, plus a chart keyed to the Revised Common Lectionary. Next Sunday -- the second in Lent, year B -- is keyed "light, sacrifice, judge."
If you can get a copy, get the Unitarian and Free Christian "red" Hymns of Faith & Freedom, again for its superlative indicies. But the only place I've gotten one is at the GAUFCC offices at Essex Hall. In person. In London. The Unitarian Christian Association says they sell them, but there's no reference to it on the website. Good luck.