When you neutralize an acid solution that contains heavy metals, you end up with metal hydroxides or metal carbonates. In the EPA's eyes, these solids are still hazardous waste, based on their method used to test them. Also, these are difficult to handle. They are very voluminous and are hard to filter and dry. They can feel dry in your hand and still contain 75% water.
I would suggest first, before neutralizing, that you cement the metals, AS METALS, using another metal that is higher on the electromotive scale, such as iron or aluminum. The results would be metal powder and a solution containing Al or Fe. Then, after removing the powders (rinse them well and prevent oxidation), you could neutralize the solution. You end up with Al or Fe carbonates or hydroxides, which are considered much less hazardous. They will, unfortunately, also be difficult to handle.