I agree with your concern, but also share your ignorance of any hard and fast regs on the subject. Stamped drawings of the design and also certification by an appropriately qualified inspector after erection are certainly a good place to start. The "30 minutes to make sure it holds" doesn't instill much confidence, though.

What would it take to make your crew feel comfortable and confident they'll all go home in one piece each day of this job? Does your company have an industrial safety expert on staff? If not, you may want to contact a consultant and have them take a look at the situation.

I've been privy to a couple of column moves/replacements inside existing buildings. Luckily none have had significant issues, but what issues did arise normally arose within the first couple of minutes/hours of the shoring taking the load. Once the shoring is in place and loaded, it's not incredibly different from a regular column risk.

That is assuming the shoring is adequately designed for the loading imparted to it. In the couple of shoring designs I've reviewed they are generally "over-designed" for the loads to provide some redundancy since the consequences of failure are quite high.

As jayrod stated above, I wouldn't worry too much on the strength of the shoring. But, since it looks likely multiple crews will be present at the same time, I think you shall ask the plant manager to hold a pre-task coordination meeting, to iron out details and safe work procedures. Each crew knows more about the other crew's task and operation, the safer the execution of the project.

Essayons RCP 23:
Retired13’s idea of a “pre-task coordination meeting,” seems like a really good idea; with the client laying down the law, that the two teams have to cooperate and work together. The column guys are the ones who changed their schedule, and know you are the one being inconvenienced. Your completion date should possibly be extended to allow you to work safely and unincumbered; an incentive to get the client to cooperate and insist on same from the others involved. Can they shore and work on one area/col. at a time, so that you can keep working, unhampered in other areas. Can you come in first and clear your old equip. out of their way to make their work quicker and cleaner; then come back to that area to install your new equip. when they move to the next area? And, move down the line this way. Will you be given some benefit/credit for doing this? You won’t even be in the immediate area while they are shoring and un-shoring for each col. Can you share some moving and lifting equip., etc. to minimize extra equip. in the area. It is fairly typical that the more contractors (individual sub-projects) you crowd into one area, the more they get in each other’s way, and the better the argument that you/they interfered/held up the other contractor. So this situation does require some special planning and management. I think plans, calcs., schedule, etc. for their work and shoring, signed/sealed by a P.E. are a min. that they should furnish to get started on this planning and coordination effort, and the owner/client should support this. Of course, you must come with your schedule and an open mind toward cooperating. This isn’t the/your military any more, where you say jump and everyone asks ‘how high’ and then jumps. It’s a bit more like herding a bunch of independent cats.

Edit: Bldg. Codes, OSHA, bldg. specs., etc. do not always cover every imaginable situation in the entire universe, although they keep trying, with ever thicker cookbook like newer eds., each less coherent, and more convoluted, than the last. You might be looking for (want to look at) some of the more general sections, paragraphs, etc. There is considerable general verbiage which suggest that designs should be done and overseen by competent Professional Engineers and Archs., with special inspections where needed; that the work should be done by competent contractors, mechanics and workmen; that the work should be done with the health and safety of the public and the workers always in mind, etc. Then, you and your attorney, and your insurance carrier make what you wish (what you will) of those general statements, to try to stay out of trouble and perform your work responsibly and cooperatively.