Can I legally be reimbursed for shipping gear back to old unit?

If you're referring to CIF issued items, you should have been cleared before PCSing, if not, your current CIF should be able to assist you with that.

If you're referring to items that you signed a DA FORM 2062 for, you will definitely have to return those items, and will not be reimbursed for your shipping expenses. If this is the case, it's unfortunate that your leadership set you up for failure, but all you can do at this point is learn from it.

If you're referring to items that you received from your unit and did not sign a DA FORM 2062, you can not be charged for those. That would be another failure of your leadership by failing to sub hand receipt those items to you. Whoever signed for those items would be held financially responsible.

In my opinion, the right thing to do is send the items back to the hand receipt holder. That's looking out for your fellow Soldiers, unlike what happened to you. It's always best to leave any items that you receive from a unit with the unit. It saves the unit money and make sure that they have those items if needed.

Ah, an opportunity for your current leadership to excel.... or fail. Good stuff on what you might have had to sign your life away for but it's a no brainer for the S1 to assist in proper documentation and the Command to ship it back. I'd also have my SEL have a chat with their SEL about how not to hose over the junior ENLs. But I'm not the Skipper....

Who died and made this E-6 the boss of the NG? You need explanations, regulations, and logic applied to your situation. It sounds like it was erroneously shipped, so they can ship it back to make it right. Don't go buy one NCOs words you need your chain of command involved. You hear me?