Sounds like your battery might be suspect. To load test a fully charged battery you load it at 1/2 the cold cranking amps rating for 20 seconds. It should not drop below 9 volts. The battery in my car is 1000 cca, yours should be similar. That means it's tested with a 500 amp load. If your fully draining the battery in 3 attempts at 350 amps, it sounds like your battery is weak. A weak battery will cause the amp draw to go up. It will also over heat the starter causing it to fail.
If your battery checks good, the initial draw when you first hit the key should be around 350-400, but this should drop to around 175-200 after engine starts turning. If it remains at 350 that's too much. Your bushings are probably worn causing the armature to drag against the field windings. If your handy with tools the bushings & brushes can be replaced for next to nothing.

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