After clearing the base game with a bunch of characters by now, I'm rather surprised to report that a melee Embermage was my most successful one. Their skills are balanced for a class that is not expected to go into melee a lot, so if you specialize into it it gets really impressive. Magma Hammer in particular is this strangely amazing jack-of-all-trades skill that any other class would die to get their hands on. AoE? Check. DoT? Check. High stun chance? Check. Shield breaking? Check. Attack speed debuff? Check. The burn has its own icon but it still counts as setting enemies on fire, so Fire Brand damage procs on it, which is pretty incredible. It's like the Engineer extra lightning damage on stunned enemies, except it's based on level rather than strength. Fire Brand is maxed because I Magma Hammer everything all the time, but the base damage on Ice and Shock is good enough since those typically only activate when the Elemental Affinity random debuff aura kicks in. Kicker is, if an enemy's too dangerous to stay close to, you can Hammer them once, Phase away, and chunk them with a crossbow or something, because ranged weapons proc Brand damage too. None of my Outlanders with ranged weapon specialty get close to that kind of single-target DPS, even taking crits and Blade Pact into account.
Using staves and Staff Mastery would probably make the whole setup even nuttier, but I found having a shield on is pretty damn important in terms of not getting blown up by everything, so I usually go with hammer and board. (Slow weapons are good because Brands don't seem to proc more than once a second, so if you've got say one attack every 0.8 seconds you actually lose a ton of DPS.) Immolation Aura's a rad defensive skill but even 15% across-the-board damage reduction will only take you so far in Veteran and upwards.