[PDF]

I'm not sure your method is "fair". I mean, having the average of the cost of an Abysian Blood mage, an Atlantian Water mage, and a Vanheim Smith is not a good estimate of a random mage, because variety/flexibility itself is a thing that should be paid and that noone in my 3 examples gets.

What is the nearest thing to a random-5 mages I think of is Arco Mystic, but he has only 3 random elements + 2 fixed Astral . He costs 180, and is usually considered rather underpriced.
I'm not sure a random-5 mage would fit thematically anywhere or be "balanced", but I suggest a cost of at least 240 gp.