what des it take to stroke a 360 to 408?

You seem to have some time invested with him but the results are not promising. I also work out of my garage so I'm not down on hobby guys. I am one and I have my share of crap that happens. If you're having issues and he's recommending what you're saying I think it may be time to seek another opinion. The fact that you are posting leads me to think there's some doubt there.
If you are set in standing with him (I admire the loyalty) then he should be able to tell you what cam will work with the heads as they are currently sitting. Some quick items I would be concerned with... You need to have a thread or two, no more than that, showing under the rocker where the adjuster screw comes through. This should be how it is with the preload properly set on the lifters and the right length pushrods in use. So regardless of the cam, make sure he gets that right. The valve job sets the geometry on a mopar and the pushrods just connect the lifter and rocker. Too much adjuster under the rocker leads to lost lift and lots of instability that will hobble even milder cams. For sake of simplicity, I'd recommend the XE268 and get the valvetrain set up properly. Then see how it runs and move forward.