Modern index shifting is always going to require pretty fussy settings. And, Brifters are notorious for being the most finicky of all shifting mechanisms to set up for perfect shifting. Still, millions of users can tell you they are great... it can be done... and it ain't even Rocket Science (well, not quite, anyway).

I'm going to assume you are using a Triple front derailleur. Although old Campy NR triple cranks used the standard Record Double front derailleur, a Triple front derailleur REALLY helps when using modern components.

A few basic preliminary things to check for the FD set-up which could be effecting things:

Is FD set too high above the Largest chainring?
Set the clearance of the FD outer cage plate so it is only around 1 to 3 mm above the Largest chainring.

Is your FD outer cage perfectly parallel?
Make sure the FD outer cage plate is perfectly parallel to the plane of the outer chainring (when sighting downward).

Are the clearances between the chain and the inner sides of the FD cage plates set correctly?

Chain on Largest cog & Inner chainring:

Set the FD Low Gear adjustment screw so the chain is only around 0.5 mm from the FD inner cage plate in this position. (...you can set this before even connecting the cable.)

Chain on Smallest cog & Outer chainring:

Again, set the FD High Gear adjustment screw so the gap between the chain and inside of the FD outer cage plate is only 0.5 mm.

Combining modern Campy and modern Shimano components should not present any problems... Although the design of Shimano derailleur cages, and the spacing between chainrings on the cranksets are "optimized" for the pull of the Shimano shifting mechanism, it should not be different enough to screw up the shifting as you describe it. And the pins and ramps of modern chainrings do a lot to help a chain climb up onto that large ring, so don't give up hope.

A couple more thoughts...

Is the chain too long?
Make sure your chain length is correct for the Rear derailleur being used. Check the manufacturer's recommendations, but basically when the chain is set on the smallest cog and the smallest chainring, the rear derailleur pulley cage will be at it's most "relaxed" position... The wrapped up chain links will now be running basically in a horizontal line below both pulleys (since the lower pulley will now be tilted back below the rear derailleur in this position) but the slack chain should never touch the pulleys above it.

And check that the chain gap (distance of the chain from upper pulley to the sprockets) is good - this is where that "B" adjusment screw for tilting the angle of a rear derailleur comes in.

All of this stuff is really pretty insignificant on old friction shifting, but all of the finicky settings of both the front and rear derailleurs are very important with modern components. And even those silly little cable adjustment barrels on the down tube derailleur cable housing stops really are useful for "finessing" the trim.

Once you get everything functioning harmoniously, you can be the judge whether the seemingly excruciating initial set-up is all worthwhile or just to quirky to be bothered with.

Personally, I prefer simple Rivendell-style pure friction shifters on bar-end pods, downtube bosses, or even stem shifters...

but I'm just getting old and stubborn and lazy.

Good Luck Amigo!