I wasn't able to do this directly with applescript. But I did accomplish it with a combination of applescript and a file maker script.
I use applescript to create a file-maker-style file path in a separate text field. The file maker script then inserted the matching file into a container field. So my applescript looks, roughly, like this:
set theFilePath to choose file with prompt "Please select your file:"
tell application "Finder"
set theFile to file theFilePath
end tell
tell application "FileMaker Pro"
set theRecord to create new record at database "MyDatabase"
tell theRecord
set cell "filePath" to "filemac:" & POSIX path of theFile
end tell
do script "File Linker"
end tell
The corresponding file maker script is (the container field is called "file"):
Go to Record/Request/Page [First]
Loop
If [ not MyDatabase::file]
Set Variable [$filePath; Value:MyDatabase::filePath]
Insert File [MyDatabase::file; "$filePath"]
End If
Go to Record/Request/Page [Next; Exit after last]
End Loop
Works like a charm.