... but I only have a multimeter with diode tester to work with so it is hard for me to do any testing.
I have a couple shelves filled with various test equipments and the truth is that, faced with this scenario, the Multimeter would be my test instrument of choice here.
*You know that something *after* that resistor is drawing too much Current.
Ohm's law plus the Resistance scales of your multimeter, along with the radio's schematic, you should start looking for the path of low resistance to Common in the circuits following that resistor.
Since the rig is blowing fuses and thus cannot be powered up, there are really no other pieces of test equipment that could be used here. You gotta find the short and the multimeter along with the gray stuff between your ears is indeed the instrument of choice here.
Hopefully the fault lies in some other component other than the finals.