1. Collecting quotations of earlier paytanim in piyyutim of later paytanim.
2. Research into prayers surrounding the Priestly Blessing. Today's Ashkenazic machzorim have the prayer about the dream, from the Babylonian Talmud, and the one about the 22-letter divine name, (ostensibly?) from Sha‘aré Tziyyon of the 17th-century Kabbalist Nathan Nete Hanover. Were there other such prayers, and are there many different versions of these prayers? (Certainly there's the fact that 19th-century editors, uncomfortable with Kabbalah and divine names, removed the name from the second prayer, even though the name is the whole point of the prayer.)
3. A study of the Biblical verses that are presented before the various poems in Ashkenazic Selichoth rites. The selection of verses are inconsistent even for the same poems among the different Ashkenazic rites. Where do the verses come from -- do any of them come from the authors of the poems? Has anyone gone through the verses to determine the relevance of each one to the poem that follows? (Probably not a project for me; I'm not so interested in Selichoth.)