What do you mean by “redesign”, if you mean align to latest imagery the I see no problem with that. Again "abandoned" is incorrect here since nothing has been abandoned, maybe was: but not abandoned because abandoned implies that some part of the old structure remains and is no longer being worked on. These are likely to be worked on in the future as in removed since it’s in an active construction zone so abandoned is incorrect here. Since the road is closed and in an active construction zone I feel it’s best tagged as construction but if that tagging sits so badly with you it’s better removed altogether. 

And there is still the issue of this being a project between fdot and mdx so since I am it sure that everything mdx does is public domain I am not sure that the website used as a source is compliant with OSMs license and thus might not be able to be used as a source.

Again if a bit of road is marked as under construction it is implied that it is closed and only construction workers are allowed in there so construction tagging implies the road is closed. 