it seems that the first two videos both correspond to the first movement (Allegro). The soloist is Andrei Romanov.
The third video corresponds to the central movement (Andante) played by Maria Eshpai.
I hope someone will provide the "Final. Allegro Vivace"
Yes, that's something like what I feared; can find no obvious piece on YT that could be the completion of the concerto, nor is it featured at the other source for Russian music, Classical Music Online.
Nice idea, Mr. Henderson - thanks for trying !