We are planning an offshore trip. It it possible to empty our (waste) holding tanks overboard (once sufficiently offshore)?
Yes, but unless it's already installed, you'd need a y-valve in the TANK pumpout line, with hose coming off one side of that y-valve going to the deck pumpout fitting, hose coming off the other side of it going to an overboard discharge pump (electric macerator pump or manual diaphragm pump)...from the pump up and over a vented loop to a below waterline thru-hull.
Under the sink in the heads, There are valves with settings for holding tank or overboard. But that seems to apply to the handling of new waste being created, I.e. Where does a new flush of the toilet go.
IF the plumbing is installed, that setup gives you a choice of flushing the toilet directly overboard or into the tank.
Is there a way to pump out what's already in the holding tank overboard too?
Yep...what I described above. I suggest you get some knowlegable "eyes on" help in determining what plumbing is already installed and what needs to be installed to do what you want.
It seems to me when I move the valve to open the overboard path, I'm closing the holding tank path, so I'm not sure how anything can get out of the tank.
That setup only lets you flush directly overboard, you'll need the plumbing I described above to dump the tank.
However, If the plumbing isn't already install to let you flush the toilet directly overboard--and I'd bet real money that it isn't--I'd have it installed so that you don't have to mess with dumping the tank while in open sea outside the "3 mile limit." It's not hard to install (you will need to include a vented loop in the line between the valve and the thru-hull), and will make your life much simpler. Use the tank only when you have to.