The impossibility of rewriting the past is a principle so general that it doesn't depend on the branch of the physics, electromagnetism, Q. mechanics, whatever you want.
Is that LET compatible with FTL communication . . .?
For building an FTL communication scheme you have to show a phenomenon that while in some frame of reference (at rest with respect with the aether) the laws of physics are respected, while in another frame some laws aren't.
But if it isn’t compatible (with FTL), then how does it violate LET ?
You seem to connect the aether assumption with the FTL, in the sense that no FTL implies no aether. With aether or without, rewriting the past is not allowed in our universe.
And what’s the minimum difference between STR and some version of LET which tolerates FTL communication?
a) Bohm's mechanics seems to require a preferred frame of coordinates (it is not sure). However, until now, no experiment were predicted to imply FTL, because the statistical predictions of Bohm's mechanics are the same as of Standard QM.
b) Which version of LET implies FTL? You have to indicate such a version. So, indicate a scheme of FTL communication in base of the existence of the aether, and then we'll examine the difference w.r.t SR. In particular saying, some people try(ed) schemes of FTL by exploiting the non-locality displayed by quantum entanglements, without any LET. (Each one of these schemes were proved to be wrong, even without using the argument that the past cannot be re-written.) So, if you know a scheme due to LET, we will examine it.