I'd like to suggest is some kind of countdown sound effect for the last 5 seconds of the turn time (turn timer only, not ready or retreat timer).
I imagined some "beeps" for 4s, 3s, 2s and 1s and a "buzz" or something when the time is up. 5s is the time when the hog says "Hurry!", so no beep there.

I have 2 basic ideas. Here are to mock-up sounds for you:
Countdown_example_1.ogg
Countdown_example_2.ogg

Here you find the single files

I am not sure if these sounds are good enough for inclusion (this is mostly just an example to demonstrate you of what I was thinking), but I will upload the FLAC files on request.