The Sundays after Trinity offer a good opportunity to offer a sermon series focusing on a biblical book or theme. I have reasons to be reluctant to abandon the lectionary provision. When we were last in year C I took the opportunity to exposit Paul's letter to the Galatians, following the lectionary provision. I covered the passages that the lectionary omitted in the evenings. A similar series on the Old Testament is harder to do because we have pew sheets that follow the "related" OT provision.
Here is a first draft of a series on covenant institutions, using the lectionary provision creatively.
29 May (Proper 4)
1 Kings 8.22-23, 41-43 - temple: the particular and universal God
5 June (Proper 5)
1 Kings 17.17-24 - prophecy: the death and resurrection of the people of God
12 June (Proper 6)
2 Samuel 11.26-12.10, 13-15 - monarchy: power and submission
19 June (Proper 7)
Galatians 3.23-29 - law: preliminary rules from an eternal God
26 June (Proper 8)
1 Kings 19.15-16, 19-21 - covenant: form and freedom in relationships