I would "place in service" the new asset and depreciate it by itself.  Then remove from service the old office to stop its depreciation.

IMO, unless there was a construction loan or the mortgage was refinanced and the cash-out was used to build the new structure, no more interest allocated to Sch C.  I guess I could maybe see an allocation for interest on the land but I'd have to give that some thought.

RE taxes would depend on your local assessment.  Some localities break out and assess structures separately.  If that's the case you can see exactly how much the tax is on the new structure and deduct that.  If not then you're allocating.