You can definitely rearrange column order in Outlook 2016 (and earlier). It can be done by drag and drop (and I'm just mentioning that in case anyone would want to ask an assistant to do the reshuffling since it happens so seldom).
Via Screen Reader I'd do ALT+V (View Tab), AC (Add Columns ribbon option), ALT+O (Go straight to the Show these columns in this order control). Find the Subject column and select it, then activate the "Move Up" button once. It should now be shown and announced ahead of the sender's identity.
Brian - Windows 10 Home, 64-Bit, Version 1803, Build 17134
A great deal of intelligence can be invested in ignorance when the need for illusion is deep.
~ Saul Bellow, To Jerusalem and Back