Well first you disabled OFDM, which should drop minimum bss rate from 6 to 1Mbps, so the disablement of bss-minrate shouldn't have changed anything. But I don't know what an AP actually does in this instance.
Minimum rate of OFDM is 6Mbps (11g). If not enabled minimum rate is 1Mbps (11b).
By rasing min-rate you try and help the 9090 to change AP at a different time, i.e. distance from the AP. What I think others here are probably thinking is that maybe the 9090 are roaming either too much or too little and that's causing issues.
So we've told you to raise bss-minrate to 12, 18, 24 or higher to provoke 9090s into a roam at a better time (read: distance from AP), however you need to be careful because you actually don't shrink AP cell size with that, just the distance a 9090 will still connect at so you 'trick' your 9090 into a roam and hopefully another AP is there with enough signal to give the handheld 18Mbps when it decides to do that.
This however is highly dependent on what your 9090 does. Since you are using archaic handhelds things probably won't work as you'd expect and enabling OFDM only and raising min-rate will probably not change anything, like you've found out.
Another thing is how APs are placed. They might be spread to thin or too close. Either way you can run into problems. That's why proper installers take allot of care in designing a WLAN network. If they are smart, they even document stuff and give you all the measurements and everything.
The only thing that would make sense in this case is your DTIM setting which if I understand is helping, which is logical since that's rate-independent.
But there are greater and greater benefits of using OFDM. It has to do with the speed that some frames are transmitted at, cell-sizing, roaming, etc. Too much for this post, but the general rule now is to use OFDM only with higher minimum rates. Not applicable everywhere, but like 95% of implementations.