I'd like to throw in a few cents, maybe just 2.
I love your original list
OP. The Judicator Battalion has always been my favorite formation in the codex. The way I run it to pretty great effect is 2 Stalkers, 2 squads with rods

,and one Night Scythe. I never really start the Praetorians in the
NS just because I want them on the field and dont want to risk not getting my reserves rolls. This gives you the benefit of a flier with the battalion bonus and the two stalkers makes it more difficult to "shut down" the formation. The problem with some Necron formations is they have one key unit that will get targeted by anyone who knows what they are doing (I.E. Stalkers and Spyders) and that makes the formation much less threatening.
I'll reiterate what @Akar said Zahndrek is great in warrior-scentric lists and helps when you have a flier to get on the board.
As far as the lychguard go,. I think you have enough dedicated assault in your praetorians that you wouldnt really need them. Lychguard are awesome and all but the challenge is always getting them close to something. People run them with Orikan in a
CAD with a Night Scythe and that basically ruins everything it touches but just lychguard by themselves is not very threatening.
I love your original list and with your permission I think I will try and piggy back off it for my own games.