April 11th is the also the day that Lincoln gave the speech that convinced Booth to carry out the assassination.
The amount of constituency, so to speak, on which the new Louisiana government rests, would be more satisfactory to all, if it contained fifty, thirty, or even twenty thousand, instead of only about twelve thousand, as it does. It is also unsatisfactory to some that the elective franchise is not given to the colored man. I would myself prefer that it were now conferred on the very intelligent, and on those who serve our cause as soldiers. Still the question is not whether the Louisiana government, as it stands, is quite all that is desirable. The question is, “Will it be wiser to take it as it is, and help to improve it; or to reject, and disperse it?” “Can Louisiana be brought into proper practical relation with the Union sooner by sustaining, or by discarding her new State government?”
Are you suggesting that Lincoln is publicly suggesting that some former slaves should have the franchise, while privately suggesting that they be sent to colonies?
Regardless, this is an idea that obviously intrigued Lincoln at one point. It would not shock me if he had explored it again in his second term. But, as others have pointed out, participation would have been voluntary, and it likely would have gone nowhere again.