Shocks won't help, as they don't "suspend" the car. Some folks use air shocks to "fix" the problem; I consider that yet another band-aid fix. As Ron suggests, you need to look at the front suspension as well as the rear.
What spring did you use to replace the old one? "Stock" or "heavy-duty"? I've long had the theory that the ever-heavier "Federal" Spitfires -- with the rear frame extensions and heavier bumpers and overriders -- were often just too much for the stock spring. I've no conclusive evidence to prove my theory, except that I've seldom seen this classic "sag" on MkIV Spitfires with the same swing-spring (albeit with the shorter rear axles), nor have I seen much of it on early 1500s.