"What could I be missing?"

Battery Cables and connections, ground to frame often overlooked. Checking switches with a multimeter does little good since it can show 12V but does not show how many amps it can carry, perhaps not enough to cause the solenoid to make a good hard hit.

I suggest you quit spending money and spend a little time checking. Have you tried jumping directly from your new battery to the starter? Use only one jumper cable at a time then both. Have you tried jumping from the battery cable terminal on the new starter solenoid to the small terminal on the solenoid? Does your new solenoid have two small terminals? IF so is one of them grounded? These will help isolate where the problem may be.

Walt Conner