It sounds like you have a few things left you can try.
1. Tighten the CAN receive filters to only allow the messages you need
2. OR switch to NI CAN frame API's. These will give you better control over the configuration, including the ability to set custom buffer sizes, better filter options and faster response times. The big downside of NI CAN frame API's is that they require you the programmer to do all the work, so they are harder to learn.
Check out the example code link for the example code NI CAN example using Frame APIs, it is submitted under third pary examples.
NI CAN example using Frame APIsThe example was written to use CAN buffers (at the speed you need, you will probably need to use buffers) You can probably get response times down into the 1 to 2 mSec range if you do it right.
For the second problem, whenever you get that error about CAN comm warnings, try doing a CAN close and CAN reset, most of the CAN reads and writes will not work if there are errors.