Money is really what JWs worship, despite any claims to the contrary.
The Necessary Family Business™ clause proves it with utmost certainty. If your ex-wife felt so strongly that any influence of yours was so harmful to your child, she wouldn't accept the money, nor would the WTS encourage it. If they were compelled to endure financial hardship for the sake of The Truth™, then the WTS would likely have to set up a fund to assist single parents who divorced on grounds of Spiritual Endangerment™. Your money suits their agenda just fine.
Would you have the right to require an accounting of how the money is spent? Do you get to claim alimony and child support as a tax deduction? I'd get it in writing from the court that the ex must supply you with receipts. You don't want one thin dime going in the Contribution Box™ - all of it must be used for essential expenses, such as clothing, food and shelter.
Are the maintenance payments enough to allow her to not have a job and Pioneer™ instead? If that's the case, then I think a review and possibly a revision of the support order is a reasonable thing to request. Is she making substantial Contributions ™ to the WTS using your support payments to do so? Again a review is in order.
If you do succeed in having the payments decreased, set aside the amount you've saved in a trust fund for your child's education. Tell the court that is your plan. You know the WTS would rather have that money for themselves, and you need to think of your child's long term benefit.