My first instinct was what a sad situation but not one that you could seriously lay blame on the school for.
Then, I read your second post.
I believe the issue of responsibility lies in the personal items that you lost as well. If they were important to you then why would you have left them where dozens (understated I am sure) pass through daily? Your items are your RESPONSIBILITY. We teach our children that everyday. If you care about it, take care of it...
I worked at a restaurant many years ago, and I took off my rings to help with making the hamburgers and then left them on the shelf, wrapped in a paper towel. One of those rings belonged to my mother and was opal. The others were also fairly sentimental and worth something (not gold, silver but with gems)
They were thrown away because they were mistaken for garbage. Sure, I wondered how someone could mistake a very heavy jangly piece of paper towel for garbage but when all was said and done, the rings were my responsibility. I didn't ask anyone to look after them, I left them there by mistake. But it didn't change the fact that they were my responsibility.
Now, secondly, I have to ask you, why are you in your school's PTSO? What do you raise funds for? What is your purpose??
If any part of your answer is the children, then to bill the school wouldn't exactly benefit them would it? If they need to give you $180 out of their budget, where will they get the $180 to replace it? Seems like a lot of hassle and worry just to make a point.
I realize that a lot of hard work went into the labels and I realize that it upsets you. I've been there as you have seen many have. But what you do next is the big question now.
I assume that the trash had already been collected when you discovered this had happened, so now, you can't get them back. It is unfortunate but it happened and it's over. Like others have said, it's a learning experience. Perhaps if you don't have the room to store them at home and you don't have a place in the school where they can be held securely, that you put the word out that you need a corner somewhere to store them in. I'm certain that someone would be happy to put them in their garage, basement or elsewhere. If there is a concern over how the money is handled and that it's been handled inappropriately, then this would be a great time for your board to review your financial policies. There are excellent methods available all over the boards and everyone here would be happy to share with you guidelines, audit methods, etc.
It is time to let go of the anger over this though. It's not doing anything beneficial for anyone, especially yourself. Take a deep breath and start over, a little wiser. But to dwell on it, harbor anger over it, to bill the school and alienate the staff and the ever needed custodians, it's just not worth it.