Yes, you pay only the difference with the amended Form 1041 (no Form 1040-X just a checkbox on Form 1041). The IRS will eventually connect all payments, original return and amended return.
Per the Form 1041 Amended Instructions (page 20): If the total tax on line 24 is larger on the amended return than on the original return, you should generally pay the difference with the amended return. However, you should adjust this amount if there is any increase or decrease in the total payments shown on line 26. Make this change before you mail the return either in Forms or after you print it for mailing.
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