I did look into the line with 6...Qa5 a while ago - it appears to be a novelty, but since Stockfish gave it as 0.00, I thought it could be a solution.

Then I checked it with Leela and decided that 7. O-O b5 8. d4! b4 9. Nd5 Nxe4 10. Bc4 Bb7 11. Re1 is an exceedingly dangerous gambit - i.e. 11...cxd4 12. Nxd4 +/- or 11...Ndf6 12. Nxf6 Nxf6 13. c3! with a strong initiative.

Unfortunately, I think Black has to look elsewhere for equality - after all, it shouldn't come as a surprise that a lack of kingside development would be swiftly punished.

Thanks for the link, BeeCaves - I actually wasn't aware of Carlsen - Wei Yi 2020. However, the fact that Carlsen crushed Wei Yi after 19. Ra3, when 19. Bb4! is even stronger,  does not bode well for the entire line with 11...Be7.

Instead, Leko's 11...Ng4 is very interesting. After 12. Bg5 h6 13. Bh4 Rc8, the bishop has been pushed off its most dangerous diagonal, so the b6 pawn is safe for now. The ideas of kingside expansion with ...g5 and/or ...h5 are also attractive.

Unfortunately, I don't think this is an easy equalizer for Black, and in fact I'm not sure it fully equalizes at all. White has a variety of interesting positional tries, and Black has to be very precise to hang on. For instance, I don't even think 14. Nd2 deserves a dubious mark - after 14...Nge5 15. h3! Black has to be careful not to fall into the trap with 15...g5 16. Bg3 Bg7 17. Nc4!! Nf3+ 18. Bxf3 Bxd4 19. Nxd6+ winning.

In that specific line, however, the careful 15...Qc5!? should be fine for Black. Thus, in my opinion, the real critical line (which I couldn't fully solve) runs something like:

13...Rc8 14. h3 Nge5 15. Bg3 Be7 16. Rd2!? Nxf3+ 17. Bxf3 e5 18. Qd3 h5 19. Qf1! +=

That's a lot of weird computer moves from both sides, but such is modern chess. Black has a surprisingly tough time dealing with the weaknesses in the position, and if the dynamics don't work out I think Black may just end up statically worse.

The Moscow with 3...Nd7 4. a4!? is quite the trendy variation, but while analyzing it recently I have been surprised by just how strong it is. White plans on squeezing Black with the a4-a5 push (i.e. 4...Nf6 5. Nc3 g6 6. a5!), so the principled reaction has to be 4...Nf6 5. Nc3 a6 6. Be2 b6, stopping this plan.

Now White plays 7. d4 cxd4 8. Qxd4, when the fight will revolve around the weak b6 pawn. Black has a choice of set-ups:

1) 8...e5 9. Qe3 Be7 10. O-O O-O 11. Nd2 Bb7 12. Rd1 Qc7 13. Nc4 Nc5 14. f3 has scored very well for White. Stockfish prefers 12...Nc5, but after 13. Nc4! Black still suffers:

13...Ncxe4 14. Nxb6 Nxc3 15. bxc3 Rb8 16. a5 Qc7 17. c4 +=
13...Nfxe4 14. Nxe4 Bxe4 15. b4 Bxc2 16. bxc5 Bxd1 17. Bxd1 bxc5 18. Bd2! +=

2) 8...e6 9. O-O Bb7 10. Rd1 with another choice:

10...Be7 11. e5! Bxf3 12. exd6 Bxe2 13. dxe7 Qxe7 14. Nxe2 O-O 15. b3 +=

10...Qc7 11. Be3 Be7 12. Nd2 O-O 13. Nc4 d5 14. exd5 Nxd5 15. Nxd5 Bxd5 16. Bf4 Qb7 17. Nd6 +=

For the moment, I actually don't see any clear way to equality for Black. There are numerous transpositions in the variations above, but White's plan is rather straightforward (i.e. some combination of Rd1 and Nd2-c4), and there don't seem to be any effective move-order tricks.

If 4. a4!? is really this effective, then 3...Nd7 is under pressure as an entire counter to the Moscow Variation. I would rather play 3...Nd7 than 3...Bd7, so I ask those of you who have analyzed (or are willing to analyze) this variation: what is Black's best response?