There are calming collars made by Feliway. Put one on each. Also, Feliway concentrated spray. I use it and SWEAR by it!!! Everytime there is a tussle between any of my cats, I spray it in the air. Calms them down instantly.

Instead of a time out, how about just letting them work out their issues, while you are present with a spray bottle. It COULD be that the stray kitty that's near your wood pile has "marked" the wood with his scent and that is what is causing havoc with your two.

Feliway is a God send to me!! Whenever I have a newbie come in, I keep both handy.

If both have tolerated each other up till the stray started coming around, that could be the problem.

Good luck. Please keep us posted. If you need help getting calming collars, let me know. They can be purchased on Amazon for about $10, or at any pet supply store.