When traveling to the right or, worse, upper right, the large, blocky minimap makes seeing enemies difficult, let alone targeting them. It’s not a question of size, really, but more of the box that the minimap is in.
My suggestion is to take from what we know works in MMOs: a round, clockface type structure for the minimap with small “+” and “-” tabs attached (emphasis on small).
There is no avoiding that the map will be in the way regardless of size; that’s inherent in the feature and what it adds more than makes up for it. But its obtrusiveness can be minimized by using the MMO map technique.
Since the quest log adds to the blockiness, I would also suggest making its font smaller, making its window borderless and left-aligning the text.
Taken together, I think this would bring some visual relief to the player.