Well in this period Poland was a bit of a punching bag, fragmented since the 12th century or so and losing territory from every side (Pomerelia, Pomerania, Silesia, Halych, etc.). It could only really start on eastern expansion in the mid 14th century, at which point I doubt the situation in the southern Kievan Rus would be as advantageous as it was during the 13th. Moscow is in a similar boat I'd say, if anything it unified later.
Halich-Volhynia is possible. Their eventual disintegration in the 14th century was kind of luck dependant, since it took both of their princes (presumably) dying to the Tatars in the same battle to start their succession crisis and partition. Just the fact that Lithuania isn't there pressuring from the north and plotting with Polish kings to control Halich-Volhynia would give them a boost, although it's still possible for them to end up in some unfortunate succession and then lose out to Poland and Hungary pressure.