This seemed to work well, but eventually the system became too much of a burden. We have proposed to the management to fix those problems once and for all, by upgrading the whole network - the wireless APs and the networking equipment. Eventually they have trusted us to carry out this upgrade and so we began our quest for delivering a better, more stable wireless signal to every room.
We already had some insight on which rooms struggled for signal, so we did a basic survey to make sure the new access points will do a better job delivering the much needed Wi-Fi signal to those rooms. User devices usually emit a signal that is much weaker than the signal emitted by the access point. That is why sometimes on a mobile device you can see a strong signal from the network, but cannot connect to it. This problem is resolved by placing APs closer to the user devices. Having done that, we now had to pick a proper network switch to interconnect all of the devices and provide power to the wireless access points. We went with the obvious choice and used Ubiquity's Tough Switch. The use of Power over Ethernet switch allowed for much tidier setup as the switch is now a central point of network connectivity and power distribution to all of the APs.
With all the APs powered up and interconnected we went ahead with the channel planning. Every AP operates at a specific channel. Nearby APs must use different channels so they wouldn't interfere with each other. Lowering the output power of the access points also helps reducing interference and prevents unnecessary connection attempts of distant users to the network. We also implemented basic quality of service using Mikrotik's simple queues. This way the available bandwidth is shared fairly between all the connected devices.
It now has been a bit more than a month since we did the upgrade and we haven't received a single complain, which is a big improvement over the previous system.