I have had back-to-back stays successfully post as separate stays. I just told the hotel front desk that they need to be done as separate stays because I was paying for some nights and the company was paying for some nights.

But I was not doing them as reward nights. Nor was I doing it to qualify as a promo. So I can't say for sure if it will work for either of those.

I was doing it to build elite bonus points. It was something like 1K or 5K bonus points for each stay (not per night). So I just booked two stays with bonus points, back to back. Told the hotel that I needed to officially check-out after the first stay because I was paying, and the company was paying for the rest. I got the normal points for the nights, and the bonus points for both stays.