I'm not a big fan of directionals, other than for outdoor p2p links.
I think first of all, I'd seek to understand if the user count of 200 is realistic and reasonable from a business perspective. I.e. sure they don't want to expand it to the full seat count ever? Really?
If it is 200, and the customer can afford them, 8 x AP225 (or similar) would be fine I would expect.
The 8 is based on maximum non-overlappers available to us in the UK for example. Not sure what region you're in?
Based on 8, that's about 25 clients per radio. Of course, you should check all the normal "bandwidth/application" demands bits.
Then consider only enabling 3 or 4 of those APs for 2.4ghz if desired (maybe by AP group)?
Mounting them under the catwalks facing directly down into the seats should be fine. You might want to do an exercise where you check the SNR at ground level and tweak TX powers down a bit, but you shouldn't REALLY need to if the channels select correctly automatically?
#AP225