All good advice..
I have done it with a TIG welder, works good.
Take your time, and if you have to add more than one pass of weld bead add about 1/2" or so of metal the thickness of the whole door edge, this helps to be a heat sink and reduce warpage. Then trim off what you don't need, and sneak up on it with a grinder to get it just right without having to weld any more.

Uncoated welding rods (well a light coper coating) are sold in many sizes for use with a TIG welder, I have some from 0.035" up to about 1/8", and I know bigger is available.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-