God has always been directly accessible through direct prayer, so God has changed nothing concerning that. But as to God communicating through the OT prophets, God doesn't have to change Himself for Him to change direction. It's like Christ fulfilling the Law. It doesn't mean God changed.
I don't see to many references in the OT to that effect. The OT God appears to those he chooses to communicate with, not to every Tom, Dick or Harry who kneels down and prays. Prayer is petition, not a two way communication. That doesn't mean God is accessible, for the Bible says God will do whatever he want regardless what we say. After all, since you as a Calvinist believe in double predestination, prayer is meaningless except as a senseless commandment that will not change what God has preordained.
Obviously, the New Testament God is different in that regard. He hears you and listens to you, and in fact Jesus is quoted as saying that whatsoever you ask you shall be given. That's novel compared to the OT, don't you think? So, it seems like God changed...
It's like Christ fulfilling the Law. It doesn't mean God changed.
If he fulfilled what cannot be fulfilled, what is eternal, and what is to be observed forever (according to the Old Testament), then either God changed or someone didn't get it right while taking down notes.
This does not make sense if God can't be moved or changed.
What MOVES God that He needs to change direction?