How often does the radio sample the priority channel, or "pulse" as you describe it?
I have a TK-7360, which is essentially the mobile version of your radio, set to sample every .75 seconds and have no trouble hearing the non-priority channels. It does get a little hard to understand when set at .50 though, which I believe is the default setting. If your radio does sample every half second, you might try asking whoever programs your departments radios to increase the interval to .75 or even 1.0 seconds. Since it is an issued radio get permission first.
Priority is pretty much mandatory on any public safety radio; and I wouldn't recommend any interval over 1.5 seconds, as you are much more likely to miss important traffic on your priority channel. This is all especially true for any kind of fireground use.