Does it make sense to try to determine what portion of the house value to assign to the furnace, and what portion of the depreciation?
No. Under no circumstances should you change the cost basis of any existing asset. Doing so will completely skew the current depreciation, as well as the depreciation history on the asset.
Simply add the new furnace as a separate asset classified as residential rental real estate and it gets depreciated over the next 27.5 years. Depreciation starts the date it's placed in service.
