You may find a bank that will agree to this, but , as your recognize, it does pose a substantial risk and you may have a very tough time find a bank willing to honor multiple powers of attorney. Perhaps you can find a bank or financial institution willing to allow such deposits if you provide a bond or substantial compensating balance.
When attorneys deposit checks in their trust account, they usually are dealing with checks payable to the attorney, or with checks actually endorsed by the payee to the order of the attorney.
This comment is general in nature and is not intended as legal advice. It does not create an attorney client relationship and obviously is not confidential. You should contact an attorney in your area who can review with you all of the relevant facts and give you specific legal advice.