to prevent Rxd7+

Passive.. Kg8 or Kh8 would've worked?

To prevent the black from doing Ng6. Doesn't quite do it though but is daunting. Ng6 Nf5+ Kh8 (Kg8 loses a rook) looks playable for black.

and the defense holds.

?! the king is the last piece I have that is not already committed to the attack. Bringing it in only exposes it to a counter-attack but I could see nothing better.

or d5 for space and tempo

Re3 for a win.

? Indefensible, opens the door to the black king.

to trap the white king but not enough and too late

And black has to choose between infinite check and giving up an officer for free. Draw.