
It's really easy to record in fullscreen:
Step 1: Go to "Options" -> "HUD Settings" and tick the "Hide HUD on Action! startup"
Step 2: Restart Action!
Step 3: Start Minecraft
Step 4: Toggle Minecraft's fullscreen (F11 or in the options)
Step 5: Record!

(You can also toggle the HUD-visibility while in fullscreen, it won't crash)
The first step has to be done once.
And notice: when showing the HUD with the frames etc., the game will crash if you leave fullscreen mode.
And to those developers outthere:
I don't know if you are aware of this fact, but the game only crashes when toggling fullscreen if Action! has hooked into the rendering. If you don't ever show the HUD, it won't crash even on toggling fullscreen.
Hope this is helpful.
Greetings, Death