An ergo shifters are so complicated that a do it yourself (and even LBS) rebuild creates more harm than done and may be an expensive exercise into futility. Even campy does not have a manual for this coz they don’t advise it. Unless you know exactly whats wrong and parts that need replacing it is best to leave it be. However it is possible and bike guys at campyonly.com have done it and the instructions/schematics are available in the site.
But at this point you still don't know 100% if it’s the shifters although they're the prime suspect. What is peculiar in this case is that how come it happens only during climbing or when much load is applied. A defective derailleur (ie. cracked parallelogram) can also cause this.
What you can do to find out once and for all is to install the shift lever in a similar drive train (chorus9, centaur9, veloce9) and see if the same happens. But only do this once you are certain that your chainline is sound, the rear der. Is OK, there is no cable stretch, and the chain is still ok.
Another way to ascertain if the rachet mech in the shift lever is giving out is this. A chorus 9 speed shift lever has 8 shift points. If you are in a certain gear when the jump happens, say, the fifth gear, and it shifts a cog (going into the 4), you should have 3 remaining shifts to go to top gear. This means the shifter is skipping a rachet. But if you still have 4 remaining shifts then the problem could lie somewhere else.