Hi Laurie,
Im not a Kaspersky user myself and was hoping someone that was would pop by to answer this for you, It does sound as if the Pirmary traffic is being interrupted or blocked in some cases by it.
It maybe that Kaspersky has some other settings maybe even p2p specific settings that the security could be lowered on? The fact that you'd estimate 25% sucsess shows the ports are open, but the traffic is being messed with either by Kaspersky or by the ISP, Shaw have always been hot and heavy into throttling. Could be coincidence, but like you I'd suspect Kaspersky first here. If you have the installer for this software, it maybe a good idea to uninstall it to verify that it does indeed work fine without it.
When you used Secondary can you also verify for me that you did 'Not' adjust your WinMX Settings for Ports?