Book 2x rooms for the shorter stay period on 1x reservation ..... ++ at hotel post checkin have desk extend stay for 1x room for the extra nights on the 2room reservation.

This could result in a slightly higher rate as last week flex rate for extra nights but if you want all points on one res number that is your only real option

Just to be sure to avoid being disappointed if your hotel is sold out at checkin you can book a second flex booking for your needed extra nights that you can cancel after checking day/time although that won't force hotel to honour that rate if lower than rate on the day.
(If full cancelling free up rooms to be added.to your booking)

If not sold out most hotels will honour company rate if still available online even when extending this way, and I sometimes get same rate for extensions to my 1room bookings when hotels are lowish occupancy even if rate on day has increased slightly.


It is Not possible to have this auctioned by hotel prior to checkin as you'll instead still end up with 2x reservations