In this case the high current probably is coming from the alternator and going to the battery.
I say that because (a) he started the car with the alt disconnected and didn't blow the fuse.
(b) starting current to the starter relay and ignition should be around 5 amps.

When the battery is low after starting and at fast idle its not surprising the alternator if its half decent will briefly supply more than 30 amps to the battery.

To find out if there is a high voltage problem, connect a voltmeter to the alternator output stud or the battery positive.
During start, voltage will drop - as low 9 volts. If its down around 9 V - the battery probably needs a good charging or replacing.
Running, it should be over 13 and below 15 V, depending on temperature, the regulator and how much resistance there is the in lines to the regulator.

Bottom line, there should be a fusible link. If it was replaced because it showed damage or melted, then find the source of the problem.

Very briefly after starting, current flow should look like shown with the orange arrows.


When the battery is recharged, it should look like this.


Ballast resistor gets exrta hot with switch when the distributor is not turning because the coil is getting continuous current. It's like having the points closed.
DON'T DO THAT for any length of time. It's not good for the coil or the ecu either.