Never seen any exchanges yet that they shoulder stuck transactions while depositing on their exchange. They only make transactions once you already trade your deposit coins from their exchange and before you can trade the deposit amount it requires 1 to 3 confirmations before you can trade the deposit amount.
Can you tell us what exchange you use where they transfer and do CPFP from your deposit address to their own wallet?
I usually see all my exchange deposit address it only transfer once you already use it to any of their services.