Sadly the system where I made my previous tests is no more, so I can't try what you suggest.
Anyway, I'm now on Ubuntu 13.04 (Kernel 3.8.8 ) with backports 3.11rc3 and there are problems here too. With default drivers there was the infamous negative channel issue, with this version of backports it is gone but also is the ability of injecting packets with aircrack. On the other hand reaver was able to crack my test WPA in less than 2hrs, so I believe something is working under the hood, but not aircrack. I tried stopping all network services before starting aircrack, nothing changed, the weird thing is that the "injection test" isn't failing.
ifconfig wlan0 down
airmon-ng check kill
Found 6 processes that could cause trouble.
If airodump-ng, aireplay-ng or airtun-ng stops working after
a short period of time, you may want to kill (some of) them!
-e
PID Name
1155 avahi-daemon
1156 avahi-daemon
1425 NetworkManager
1453 dhclient
2837 wpa_supplicant
2839 dhclient
Process with PID 2839 (dhclient) is running on interface wlan0
Killing all those processes...
iwconfig wlan0 channel 11
airmon-ng start wlan0
Interface Chipset Driver
wlan0 Realtek RTL8187L rtl8187 - [phy0]
(monitor mode enabled on mon0)
aireplay-ng -9 -a 00:**:**:**:**:** mon0
Waiting for beacon frame (BSSID: 00:**:**:**:**:**) on channel 11
Trying broadcast probe requests...
Injection is working!
Found 1 AP
Trying directed probe requests...
00:**:**:**:**:** - channel: 11 - 'test'
Ping (min/avg/max): 1.504ms/9.133ms/50.635ms Power: -50.83
30/30: 100%
I'm on a newer kernel now, with a different distro and different drivers and it's still failing.
Did you resolve the injection problem on debian then?