Considering that Lincoln didn't even try there is no way of knowing that for certain.
In his inaugural address Lincoln made it clear his hope for a peaceful solution.
Meaningless lip service. IIRC, Saddam made a speech on Iraqi TV a few days before the war hoping for a peaceful solution as well. In Lincoln's case, the real message of his speech was "back down or else there will be war." That message was universally known among the southerners in the days following his speech. If you doubt me just look what they said in Congress in response to it. Even the moderates from the border states like Virginia (who Lincoln also refused to meet with) saw it as a threat for war.
He had taken no hostile actions
His hostile act, aside from all the thinly guised threats of war, was dispatching the fleet. He had been plotting that hostile act since Anderson garrisoned Sumter on December 26th.
Violence could have been avoided had Davis want to avoid it.
...which makes about as much sense as "violence could be avoided if you simply open your door and let me march in with my shotgun in hand."
To what end?
In Virginia's case, to the end of preventing it from seceding. In the case of the rest of the south, to the end of devising an agreeable means of permitting peaceful separation, altering the nature of union, or offering a compromise to counter their departure from the union.
no reason to believe that the Davis regime, having seized federal property at the point of a gun, had any interest if paying fair compensation for it.
Wrong. All three of the other forts that SC had "seized" were bought and paid for by SC long before the federal government even had a regular army. Even then, as a means of facilitating their peaceful transfer, SC offered to pay for them. They sent commissioners authorized to deliver payment in December 1860. The rest of the CSA followed suit. In January 1861 Sen. Slidell of Louisiana even went to the Senate floor to pledge payment for any of the southern forts. Davis' commissioners to Lincoln even held papers in hand permitting them to transfer payment for facilities. Absolutely no reason exists as to why they would not have paid as repeatedly offered. The only impediment to it was the fact that Lincoln, already hell bent on war, refused to meet with anyone.
Their tactic on the first instructions were 'take it or leave it'
No it wasn't. A major purpose of the meeting was to settle on a fair price itself! They were willing to allow Lincoln offer whatever fair price he saw and negotiate from there, but he refused to meet.
Again, if you would read the instructions then there is no doubt as to their purpose. Their mandate was 'the purpose of negotiating friendly relations between that government and the Confederate States of America'. Nothing there indicates that any possible outcome other than recognition of the legitimacy of the southern rebellion was possible. Your claim at negotiation involved no negotiations at all.
Meaningless lip service.
Along the same lines as your claim that the southerners would fairly compensate for property already seized, a claim not included in the mandate approved by the confederate congress BTW.
All three of the other forts that SC had "seized" were bought and paid for by SC long before the federal government even had a regular army.
Absolute nonsense and, since the Davis regime also held mints and armories and forts and facilities throughout the south with no evidence that they ever meant to pay for them, irrelevant besides.