I can not tell if your HP psu is a standard ATX unit or not. Take some measurements of the back of the unit in your case. If they are standard size (3 1/2" high x 6" wide) then the psu should fit. The Antec unit is not unusually long.
As an alternative, FSP sells a graphics booster unit that fits in a external 5 1/2" bay:http://www.newegg.com/Product/Product.aspx?Item=N82E16817104054