Is there a way to filter the database to show texts first published in a certain year (or range of years)?
Yes. Under "Add a field" select "Year written" under "Person." This should show the date written (which is usually the first publication date) if a hymnal included this information.
When I do this for 1892, the year I am most interested in, and select result type texts (or instances, same problem) the output is a long list of hymns showing dates ranging from 1523 to 1990.
The results I want are at the tail end of the fourth page of results!
You're right, these are strange results, not what a user would expect. The first in the list ("From depths of woe") can be attributed to its nature as a translation, because the earliest date is its German birth, and the last is a composite translation. The text authority erroneously gave the date of Massie's translation as 1990, so I fixed it (1854). The others in the list include a long string of English hymns. Notice how there are four hymns by Fanny Crosby that give the Year Written as her entire life span.