Normally when you get an initial crank then nothing, you'd check for a loose connection typically at the battery. You stated the connections are tight and your battery tests ok. Have you checked your ground to the block and the connection at the starter? Also if those are good you might want to check the internal contacts in the solenoid. Another failure mechanism is a bad connection internally in the battery (even a new one). This would show you proper voltage across the battery with no/low load and zero volts under high load. Just watch out that the battery doesn't explode if it is internally arcing.
When you stated the battery was good, how did you check it? Have you put a voltmeter on the battery to see what the voltage is when cranking and failing. To inspect a battery you need to check the voltage at rest and under load to confirm it's good. Under load it shouldn't drop below 9.6 volts at approximately 1/2 the rated CCAs of the battery over 10-15 seconds or so.