Here is an excerpt from the footnote to that letter you referenced:
... "three propositions which seemed to me to cover the ground of the suggestion made by you through Mr Weed as I understood it. First. That the constitution should never be altered so as to authorize Congress to abolish or interfere with slavery in the states. This was accepted."
From Wikipedia: "The Corwin Amendment is a proposed amendment to the United States Constitution that would shield "domestic institutions" of the states from the constitutional amendment process and from abolition or interference by Congress. Although the Corwin Amendment does not explicitly mention slavery, it was designed specifically to protect slavery from federal power."
So, Lincoln's first proposition as transmitted through Weed was agreed to by the Republicans and ultimately became the Corwin Amendment.
The footnote continues to the other two propositions Lincoln transmitted through Weed:
Second. That the Fugitive slave law should be amended by granting a jury trial to the fugitive. . . . '' This was amended so as to name the jury from the state which the fugitive had fled, and was voted down by the Republicans. The third resolution --- that Congress should recommend that the states revise legislation concerning persons recently resident in the state and repeal all in conflict with the constitution --- was rejected. At another meeting on December 26, Seward continued, he had offered a fourth proposition to the effect that Congress should pass a law to prevent invasion of a state, which was amended and rejected.
IIRC, Seward did publicly state that states should repeal any of their laws in conflict with the Constitution. He apparently was parroting Lincoln at that point. A number of states did change their personal liberty laws after states started seceding so as to make their personal liberty laws not be in conflict with the Constitution. I didn't realize that Lincoln had suggested it (a wise suggestion on his part).
Here is an old post of mine concerning what Seward said publicly in January 1861 (the old newspapers are very interesting and useful): link.
I do see the following in The Daily Mississipian newspaper of January 16, 1861:
Washington, Jan. 12. Hon. Wm H. Seward, of New York, addressed the Senate to-day, on the President's message. He said Congress ought, if it can, redress any real grievances of the offended States, and then supply the President with all the means necessary to maintain the Union. He argued that the laws contravening the constitution, in regard to the escape of slaves, ought to be repealed. He was willing to vote for an amendment to the constitution, that Congress should never have the power to abolish or interfere with slavery within the States.
He said that he was ready to vote for any properly guaranteed laws to prevent the invasions of the States by citizens of other States. (I think here he was talking about one of the grievances of the Southern states, that people from the North were coming down and invading farms, etc., to take away slaves. I've seen reference to this in some of the secession ordinances. Also, Southerners had been killed in the North trying to get their slaves back, but I don't know how frequent that sort of thing was. Rare probably.)
I checked in the Congressional Globe for Seward's exact words to the Senate. They were as follows:
I agree that all laws of the States, whether free States or slave States, which relate to this class of persons, or any others coming from or resident in other States, and which laws contravene the Constitution of the United States, or any law of Congress passed in conformity thereto, ought to be repealed.
Secondly ... I am willing to vote for an amendment of the Constitution declaring that it shall not, by any future amendment, be so altered, as to confer on Congress a power to abolish or interfere with slavery in any State.
Thirdly, (long paragraph follows) ... when the eccentric movements of secession and disunion shall have ended, in whatever form that end may come, and the angry excitements of the hour shall have subsided, and calmness once more shall have resumed its accustomed sway over the public mind, then, and not until then -- one, two or three years hence -- I should cheerfully advise a convention of the people, to be assembled in pursuance of the Constitution, to consider and decide whether any amendments of the organic national law ought to be made. ...
Fourthly, I hold myself ready now, as always heretofore, to vote for any properly-guarded laws which shall be deemed necessary to prevent mutual invasions of States by citizens of other States, and punish those who shall aid and abet them.
That fourth item probably stems from John Brown's invasion of Virginia.
As you say, the footnote details a second proposition, that the Fugitive slave law should be amended by granting a jury trial to the fugitive, which was rejected. And a third proposition, that Congress should recommend that the states revise legislation concerning persons recently resident in the state and repeal all in conflict with the constitution, that was also rejected. But what makes me think that the proposals were Seward's is that the footnote continues, "Whereupon the Republican members of the committee, together with Trumbull and Fessenden, met to consider Lincoln's resolutions..." If the proposals listed above were Lincoln's then why meet to consider them again when they had already been voted on? I think it's an indication that the proposals for the amendment and other two originated with someone other than Lincoln, probably Seward. And that Lincoln's three proposals were the ones listed in his letter to the Committee of Thirteen, none of which called for an amendment protecting slavery.