The idea of these dispensations which are not concurrent, but that God interacts differently with people at different times is the same thing as saying that God has somehow changed.
Rather, a right understanding the Sermon on the Mount shows that the seeming increase in harshness of the laws reveals only the original heart intent of why the Law was written in the first place. God has wanted the heart the whole time, and God added the Law because of the increase of transgressions.
The separation of Law, Grace, and Kingdom is unnecessary and against the idea of the text. God has always had a Kingdom, and the Law was said to have been added. The Kingdom was not removed for the bringing of Grace, nor will the Grace and Truth of Jesus Christ be removed.
Dispensationalism would claim that texts such as the Sermon on the Mount were to the Jews only. Nothing could be further from the truth. Rather, Jesus said that if we love Him, we will obey His commands. Surely, to be His disciple is to follow after Him. And, He who walks another way is not following their master.