Giving days away without repaying is a great idea. It tells the company you don't really need the money money..
That sounds a lot like the way we do it.
Many people like the "give-away" as you call it. But we call it a one way swap.
To answer your question, no, we can't cross shop swap. And it does take some getting used to like you said. I've found it's way easier to work your swap as your next shift, rather than go home, try to sleep, get up and come back in to work a swap. That's why the commuters usually work a double, double, single, then go home.
Metal, It actually means more than that. It means that we want more time off, not everyone is all about money. Some just want time away with family and friends.
Real, That's is the exact same way most all the commuters do it here as well. And a very few sometimes, will pick up an extra shift of overtime on their fist double day and give away that single day for an extra day off to bring it to 5 days off in a row. Of coarse they sleep like babies on their flights home. But the majority are as you stated double, double, single. Or double, single, double to brake up the double shifts (back to back doubles) or they will do single, double, double. Just depends on their schedules and shifts on which way they would want to leave to go home or coming back to work. The trades do not bother the company as they are still getting the man power.
Sorry to hear that you guys cannot trade with other groups of mechanics. That is a great perk for the single shift employees out there...