The hardest part is taking the patch panel and fixturing it so it is flush in the hole so it isn't too high or too low, and then getting it to stay where it is while it gets heated as you're tacking it in. There are cool fixturing magnets (one on each side of the panel edge) and other cool products that are made for that purpose, and worth spending a few bucks on.

But, I'd look into a set of hand flangers, or a pneumatic flanger if you think you'll use it at least a few times. A flanger will make a step down (the thickness of the metal) all around the hole, making a 1/4 or 3/8 flange, and then the patch panel will drop right down flush. Basically you're making a countersunk hole for the patch panel, and it looks exactly the same as any other patch method from the outside.. It's a lot easier to weld that way, and you don't have to worry about cutting the patch panel as precisely or worry about warping the metal as much. It's kinda cool because you can really easily tack everything in place and keep everything located properly. People have been shaving door handles like that for decades.
Body shops don't flange stuff very often any more (because it's time consuming if you're already really skilled with sheet metal) but it's great for DIY stuff when you're not a bodywork expert.