Alright, after 3 hours of researching, debugging, keyboard-smashing, and learning, I've finally figured out something that works. Because the solution I found is (seemingly) undocumented in a unified, coherent manner, I figured I would explain the process I used for any future struggling LibreOffice users:
First off, my utlimate goal was to create multiple pages of single-sided ~3x5 flashcards in Writer, that could easily be printed off and cut up into a convenient stack. I wanted to have bits of text aligned in the top left, bottom left, and bottom right corners, as well as a block of text in the center left aligned. Because of the limitations of headers, as well as Writer's lack of vertical alignment settings and polymorphism, I turned to the address label functionality of the LO Suite.
To begin, I opened up a new Calc spreadsheet, and entered in all of my information into columns. Headings went above the columns in the first row (things like "citation", "card number"), and the following rows each represented the information on one notecard.
Upon saving the completed spreadsheet, I then had to create a new database file (with LO Base): in the Database Wizard, I chose the "connect to an existing database" option, then directed the wizard to my spreadsheet file.
As soon as the database was created and registered with LibreOffice (should be done automatically by the wizard), I went to File -> New -> Labels. On the Labels tab, I chose the newly created database and spreadsheet, then loaded in all of the required data using the "database field" dropdown and button. I chose the desired paper size in the "brand" dropdown and the desired notecard size in the "Type" dropdown. (advanced options for this are available in the "format" tab.) A KEY STEP AT THIS POINT is to go to the "options" tab and select the "synchronize contents" checkbox. This allows you to make advanced formatting changes in the following steps that will be copied to every notecard.
Hitting "New Document" will take you to a Writer file. (Three seperate LO programs have been used so far. Convuluted, right?) Gray fields with your data names should be repreated in notecard frames copied across a single page. Here, you can use the generated frames to pad and position the fields as you wish. If you, like me, wish to have text aligned at the bottom, create ... (more)