Going to answer my own question here. The problem can be resolved by editing the XML.
In the <field> tag for the text field, you should have a width and a height. The height (what we're actually worried about) can be set by either 'h' or 'minH'. 'h' is for height that is static, and 'minH' is for expandable fields.
For my case, I changed this:
<field name="tfInstructions" w="196.85mm" h="6.35mm">
To this:
<field name="tfInstructions" w="196.85mm" minH="6.35mm">
The checkbox for "Expand to Fit" is still grayed-out, but on my form, it works.