Are the columns and beams healthy below the repair levels? Are they weldable below the repair levels? If so perhaps you could install new columns slightly to the foreground of the existing ones for the top two stories. Then, once you hit healthy material, reinforce the beam and beam-column connection to transfer the load back to the original columns.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

I've used modern channel sections fitted inside the lattice set, and welded to each other, with bolting through existing to new. The problem with this kind of deterioration is that you must work around the existing connections, and the new hybrid system must then all work together.

Have you thought about concrete encasement? Your building may not like the additional mass, but it is a potentially very effective and simple repair. Clean the existing steel, provide new bars and stirrups, pour new columns.

If you are dealing with a heritage condition you may find your situation further complicated by what will be acceptable to the HAHJ.

Oh, and though I have not done so myself, I am told that pressure grouting with non-shrink product (such as Sika 212, or more likely for this case, Sika 08 SCC) is an effective way to go as well... But I have a hard time picturing a pressure grouting not blowing out or having grout flow everywhere.

Looking at your conditions, I really think full replacement or concrete encasement are the best options. Potentially add a cathodic protection system to arrest the corrosion as well.

Please investigate all of the lower floors. I have a hard time believing that such advanced corrosion is confined to the top two floors, which I presume are the ones which were exposed during other works.

One more thing: Be very careful in your assessment of the deterioration. While widespread, it is not immediately obvious to me that the extent of corrosion is problematic. Keep in mind that the rust is nine to twelve times thicker than the base metal it replaced, thus you may not yet have a problem. As you say, quite rightly, you'll only know where you stand after a good cleaning.

I personally like to clear an extensive area to "free from lose" condition, and several localized areas to white steel prior to the final evaluation... Widespread deep pitting can be quite shocking in these situations, and can also make it very hard to get a good estimate of the net area of remaining base steel.