Don't forget time from landing to being on stand, and then doors open and then through. Even in the closest scenario - landing central B gates, down the escalator, straight into security and upstairs, you're still looking at being in the lounge of destination terminal at 0900. Even if you did book in advance and there was a therapist immediately available, I think you'd be too busy stressing about time to really enjoy it.

I'd relax free from time constraints - if the spa is available, great, but if not, don't let fixation on it ruin the rest of the journey.