Since I don't know much Russkiy, I can't understand the two-turn circuit of Soyuz. So I want to ask, how the Soyuz-2 upper stage would be able to send the spacecraft to the Moon? I thought it would require a rocket like Energia for Russia to do so, and recently there had been some talks to develop a rocket derived from Energia instead of pushing the Angara program.
Actually I spent some time on this already (ten years ago), and the Proton-M was just a little short to make it really work. Things are better with Angara, especially Angara 5/KVTK. I don't understand everything in the video, I rely on Google translation which is a great tool but of course far from perfect.
I think the scenario is to have a Soyuz-TMA "on standby" docked to the ISS, with some extra ablative material layers to the heat shield and maybe some extra mass optimization. Then, when the TMA crew is already in space and "on alert", you launch the Angara with the KVTK spacetug, in a way that it requires very little time and Delta-V for the Soyuz to dock it. Timing is essential because KVTK is LOX/LH2, every hour counts and having a spacecraft already waiting for the tug is the safest way to do it. Then yes a lunar fly-by with more-or-less free return (Soyuz engine can assist to shorten the return trip) is at reach.
So it can be done as long as you can insert the KVTK very near the ISS, which means a limited launch window but nothing impossible there.