After checking with our SME, Hal McAlduff, please refer to  AFI 65-601v1 for guidance on funds to use for construction contracts including A-E, see chapter 9. A-E services and the unique funding aspects of that are also covered in the DoD FMR in multiple volumes and multiple chapters.

Once you determine that you are within any of those constraints and they're using O&M; it comes down to is this a severable service or not?

If it is: you could cross FY boundaries but the contract can be no longer than a year. So based on what you stated, this wouldn't work. See DFARS 232-703-3 If it is not severable: The A-E firm can not deliver the final product (inspection results report) until the building is complete (kind of like a special study) then you could.  However, I think that it is unlikely a fiscal law attorney would buy off on that. See FAR 32.703-3(a).  Please consult with your internal legal counsel.