Alternative is to make the fledgling Russian state to disintegrate during the Time of Troubles around 1600-1610. It nearly disintegrated anyway.
As POD you can add just one of Tver scions surviving into the 1600 and making an alliance with Lithuanian nobles, so civil war in Russia will become more chaotic.
And i must agree what by the time of Great stand on the Ugra river (1480) the Golden Horde was a hopelessly backward state. Their technology and organization were outmatched even by Russians
