Summary:
Putting the queen on d5 seems like a good idea.
Rc8 seems viable, with the idea of Ne7/(Nf5)/Qd5 (see diagram).
I still need to check Nd7 and other 35th move possibilities.
Many more words will happen before I move.
Have the idea of Qd7/Nc3 (idea:Qd5), but this hangs the rook on e8...playing Qe8 just to follow up with Qd8 seems a little silly -- especially if I'm likely to move the rook to c8 at some point anyway. So I think I'll set this aside and focus on the other main alternatives: Nd7 and Rc8.
This is, for me, a hard position to evaluate. So instead, I'll look at some typical lines and just pick based on that.
First, an aside on what White might be cooking up--since in the absence of a good plan of my own, I might as well prevent White from causing me trouble. With the knight on the queenside, I no longer see g4-g5 as a significant threat. It's easy to prevent, and it opens a hole on f4 which would be pretty easy to exploit--even something like Nh7-f8-g6-f4 would probably be good. (That knight is sort of a free agent here; it's function is sort of ill-defined compared with my other pieces, so it's easy to move it around without really weakening anything.)
The other target which I have newly created is the pawn on a5. Unclear why I rewarded White's knight's journey to c5 like this, but OK. This more or less requires either the queen to stay on d8. (Defending with the rook is just not going to work in the long term, in part because of the quasi-pin of the Nd5 via the Qf3.) Other than that, there's not much going on.
35...Rc8
36.b3 -- justified tactically by 36...Rxc4 37.bxc4 Qxd6 38.cxd5. Some serious complications in the event of 37...Nc3, though, and Black has alternatives to 36...Rxc4 (...Nd7 is still reasonable, for example). I think Black has both solid and speculative replies, so I'll save my limited study time by ignoring this.
36.Be5 -- the wrong way, I think
36.Bc5 -- logically closes the c-file, covers b6, prepares various knight sorties
36.Be5 Nb6 highlights the undefended rook on c2 and the pawn on a4. Maybe 37.b3 is almost forced in which case Nxc4 38.Rxc4 Rxc4 39.bxc4 Nd7 leaves White with a tough decision at the time control, since Nxe5 is in the air, White's pawns are weak, and b4-b3 is coming. This looks really bad for White.
36.Bc5 and Black needs to look at Nd6 and Ne5. Now Qd7 looks plausible, but there's even another drawback to Nc3 which is Nb6, forking the queen and rook. (Maybe I missed that in the first line of this post.) In fact, this theme will repeat, as Qe8 is not safe either (due to Nd6 forking queen and rook). This actually look a little troubling here. Black can sort of shift his pieces back and forth (Rb8, Rc6) but these moves aren't doing anything.
Instead, I am going to pin my hopes on
36...Ne7 -- again with the idea of Qd5 (and Nf5). This is a little dangerous because of the a5-pawn, but I think everything works out tactically because of the weakness of the R@c2. But I need to check further. I'd post the critical position, for all to contemplate, but chessvideos seems to be down, hopefully not permanently as this forum has come to rely on it quite a bit. Rehosted...
35...Rc8 36.Bc5 Ne7
Here, the 37.Bb6 Qd5 is forcing but seems OK for Black, and other ideas attacking a5 are going to be critical.
(Previous experience tells me to explicitly check for Ne7 ideas in other lines, but this is again problematic because of the x-ray attack on a8 by the f3 queen.)
Anyway, this is a pretty rich and critical position, so I'm going to take my time. I still need to address the rest of this, and then also turn to the Nd7 lines.
And I'll also give Qe8 another look. Given all of the knight-fork issues, I think I may come to find that e8 is a better square than d8 for the queen, and try to defend a5 tactically with threats against the R@c2? That seems to work in those Ne7 lines--at the very least, dismissing it out of hand now seems unjustified.