Take the blower motor down and vac all you can out first it's not easy to get up in there but it can get some of the big stuff out as well as clean the squirrel cage off good you can also check the condensate drain and make certain it isn't clogged
Next get a can of NuCalgon coil cleaner and spray it up in the drain hole it will foam up and allow some of the nasty flow out
I personally put a small hose up in there and washed out some more with water under very low pressure
Aside from removing the dash and replacing the evap core that is your only options