UPS and Fedex applied this management tax also to me on the past and I never choose them as shipping method again, choosing the Aliexpress shipping usually you get lower chances to get charged by customs.
I understand you, I had to cope will Aliexpress customer support in the past and the experience was similar, is very hard to contact them and when you get in chat with an agent you don't really know if it's a person or a bot as most of the answers are long and unnatural and if you speak with a different agent you get the same sentences.
I suggest to keep trying, the last issue I had I got the money back from an undelivered product that the tracking said that was delivered, I contacted 4 times each of them saying that the issue was fixed and I will receive a confirmation email, seeing that I didn't got the email I contacted them again after 1 week, and this repeated for 4 weeks until some agent really fixed it and I got the email with the refund while still on the chat, so if they say that you will receive an email and you don't receive at that moment probably you won't receive it.
I have also read in some forum that if you have an invoice from Aliexpress that says the VAT was applied on origin you can ask the tax entity of you country to return the double payment, but probably dealing with the administration will be even harder than dealing with Aliexpress.