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Again, if Lincoln sent an unarmed, unescorted supply ship to provision Sumter, Davis would have ordered Beauregard to reduce the fort before the resupply effort could be accomplished.

You are repeating that like a mantra. It clearly isn't true based upon the actual records. Since you won't look it up yourself, I'll find it for you.

Montgomery, April 11. To Gen. Beauregard, Charleston:
We do not desire needlessly to bombard Fort Sumter if Major Anderson will state the time at which as indicated by him he will evacuate, and agree that in the mean time he will not use his guns against us, unless ours should be employed against Fort Sumter. You can thus avoid the effusion of blood. If this order should be unequivocally refused, reduce the Fort as your judgement decides to be the most practicable.
L. P. Walker, Secretary of War.

You know as well as I do that Davis ordered Beauregard to reduce the fort prior to the arrival of the resupply ships.
It would not have made a difference whether there were warships escorting them or not. Davis was not going to allow Sumter to be resupplied under any circumstance.
He knew it would probably lead to war. But he was not going to allow the continued occupation of Sumter by U.S. forces.

DiogenesLamp quoting:

"Montgomery, April 11. To Gen. Beauregard, Charleston:
We do not desire needlessly to bombard Fort Sumter if Major Anderson will state the time at which as indicated by him he will evacuate, and agree that in the mean time he will not use his guns against us, unless ours should be employed against Fort Sumter.
You can thus avoid the effusion of blood. If this order should be unequivocally refused, reduce the Fort as your judgement decides to be the most practicable.

L. P. Walker, Secretary of War."

We should notice, first, that these orders say nothing about Union ships being sent to, or arriving at, Charleston Harbor.
There's no indication that Lincoln's "war fleet" had anything to do with it.

Second, we should notice that these orders were issued long before any Union ships arrived at Charleston.

Third, we should note that on April 3, long before Lincoln ordered his resupply mission to Fort Sumter, Jefferson Davis revealed his plans to CSA Gen. Bragg in Florida:

"It is scarcely to be doubted that for political reasons the U.S. govt. will avoid making an attack so long as the hope of retaining the border states remains.
There would be to us an advantage in so placing them that an attack by them would be a necessity, but when we are ready to relieve our territory and jurisdiction of the presence of a foreign garrison that advantage is overbalanced by other considerations. "

The chief "other consideration" being that only war could drive Virginians to flip sides from Union to Confederate.
But, just in case Anderson did surrender peacefully, Davis still had Fort Pickens in Pensacola, Florida, to start war with:

"The case of Pensacola then is reduced [to] the more palpable elements of a military problem and your measures may without disturbing views be directed to the capture of Fort Pickens and the defence of the harbor.
You will soon have I hope a force sufficient to occupy all the points necessary for that end.
As many additional troops as may be required can be promptly furnished."

So, the choice for war belonged to Jefferson Davis and, yes: