Arda was supposed to be drastically changed after the First Age. This map is from the Second/Third Ages. Do the events from the First Age map currently into what is shown? Do some have to be excluded?
The First Age / Second Age boundary is not unlike the K/T boundary...
Compared to that, Second Age / Third Age isn't that different (places like Dunland and Tharbad were forested, according to Treebeard). So if you wish to make the map a bit more ageless, you could just add a few alternate names.
- Dol Guldur was Amon Lanc in the Second Age
- Lothlorien was Laurelindorenan in the Second Age
- Mirkwood, Minas Tirith and Minas Morgul are late-Third-Age-isms too.