Stolarek et al: Genetic history of East-Central Europe...

[Vinitharya]

And where did the statement that Trziniec culture significantly influenced the Balto-Slavs come from?

Umm...Trziniec (especially East Trziniec) has the strongest likely association with Balto-Slavs. Trziniec were largely Balto-Slavic like, and overwhelming majority of the samples were I2a (a branch now mostly in Western Europeans and non-existent in Balto-Slavic peoples).
If not Trziniec then who is associated with Balto-Slavs? Pushing further east? or you're going to propose west?

I will not talk about y-haplogroups, since the picture on them is changing rapidly.

Excellent judgment.  Due to bottlenecks and founder effects, it is unsuitable to use most haplogroups to determine the proto-Slavic homeland, particularly those that appear in only one of the three divisions of the Slavic people.  The only ones I would say would be Z280, since this group lacks the bottlenecks of I2a1 and M458, and at any rate their origin/dispersal are farther to the south and west than autosomal data would have the Slavs originate.  The finding of L1029 in Wielbark does not surprise me at all, as I judge it would be abundant (for pre-Slavic M458) in that area among the Vistula Veneti.  I think L260 was further to the east, in Volyn, and I2a1 in the foothills of the Carpathians in Ukraine.