Something that I am hoping to tackle in the early 2019, the existing separation of in-game messages and private messages.
I plan to move the in-game messages to the private message system, which itself is migrating to a more "chat" oriented presentation, rather than an "email" inspired style format that it has now.
Advantages of this - you can send as many messages as you like with a move, at anytime, and the the end of the very problem you just described.
edit : On your "My Home" page, it will currently show any "last move" messages you have received. This is not really an adequate solution though.