My own thoughts are he was covering as many bases as he could. He felt that the 'patriotic' one was better PR than the revenue issue. Had Florida been the initiator of the troubles, it would be a no brainer, get Pickens. South Carolina was the one making the noise though and causing the problems. Anderson going to Sumter made the South Carolinians take things a bit faster than they may have had he not done so. Then you get a virtual fleet of ships and they knew darn well they weren't all loaded with supplies so they weren't fooled. Lincoln was caught with only one leg in his pants, so to speak because the Powhatten stopped in the Keys before going to Pickens and got there a little late for the start of the fireworks show.
Lincoln had information on every little detail going on in Charleston beginning months before April. If things started there, he'd have to go along with the Northern version that included slavery because that was all 'the rage' in that area after John Brown and Mrs Stowe had their say. New Orleans was a larger and more inland port to try to take in the very beginning and Mobile's port was also further up from the Gulf and full of Confederates. Pensacola's port was just across the barrier island. Easy picking. Also there was an operational rail line from the port. While there were 3 forts, Slemmer removed the Federal troops to Pickens in January leaving McRee and Barrancas for the Confederates to use for training. The Feds had failed to 'bulk up' their numbers to man all three. Also the first and second in command were allowed to go on leave. The third in command probably, from what accounts I have read, turned all three forts over to the South. If Lincoln learned of this, it may be one reason he was thinking Pickens trying to keep them in Union hands. If it took cannon fire to do so, so be it.
Lincoln's message to Porter about Pickens was sent in secret and carried out under cover, so to speak. If he wasn't trying to do something fishy, why be secret about it?