After gleaning the internet for a solution and finding none which worked, I decided to whip up my own. Copy and paste the following code into Script Editor, and save it as an application with the 'stay open' option checked:
repeat
tell application "Transmit"
tell document 1
tell current session
refresh list their stuff files
end tell
end tell
end tell
delay (60)
end repeat
If anyone wants to follow up this with a touch of AppleScript that cycles through every connection, that would be great. This is my first AppleScript project, so woot for me!

