Exhaust leak

That's going to be really hard to do with an early A manifold- the downleg is going to interfere with flat sanding the surfaces... passenger side would be okay, but not the driver's side.
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A machine shop can do it, but they'll groan when they see the setup needed.
OP did not mention where the exhaust leak is, pass. or driver's side.
It would also be good to know what his setup is- particularly the heads. If they are later model heads with the extended exhaust port surfaces (for air injection ports, even if they're not drilled for them), these "pads" will not allow the early A manifold to seat properly; the downleg hits the bottom of the port surface on #7 exhaust port. Massive exhaust leak; or worse, a cracked manifold if you try to over tighten it.
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DON'T grind for clearance! There's a water jacket just beneath the surface- it doesn't take much material removal to break through. I know, I trashed a good fresh head this way, and I removed VERY little material. Some have gotten away with it, but is it worth the chance? Best bet in this case is to double up on the exhaust gasket to space it out a bit to gain clearance, or to run a header flange between the manifold and the head.
As far as making those shorties work, they require a relatively aggressive mod to make them fit early As, as shown in this thread:
Removing stock exhaust manifolds | For A Bodies Only Mopar Forum

Thanks. Early heads on the 273. I pulled up the old thread on what was done on the drivers side header. Looks like flange was caved in to make it fit.