This is what I should have responded with yesterday:

Most patch panel installs, whether door skin or quarter panel variety, involve a somewhat flat crown in both the horizontal and vertical directions. Regardless of appearance, all body panels will have crown in at least one direction to help hold the shape of that panel. A flat sheet of metal has no support and will flap in the breeze, so ALL panels will have crown somewhere. If we were to look at your door along the proposed horizontal weld in a cross-section view (top-down) you would see that despite appearing flat, that panel actually has crown from front to back. It looks like a slight arc. Now, anytime you apply the heat from welding, you are going to get a shrink as that weld cools. When we weld one dot at a time (MIG), each and every dot is going to pull at the metal around it, from all directions, causing a shrink. Once you've added all those shrinks from all those weld dots together, along the entire weld seam, it adds up to a substantial amount of shrink such that what used to look like an arc is now more closely resembling a straight line. So given a weld seam like that, without any planishing to counteract the shrinking, you will see the panel pulling inward, as the crown at the weld is shrinking. Looking at the panel as a whole, unchecked shrinking would appear as a pronounced valley, where the weld seam is shrinking and pulling the adjacent panels along for the ride. Don't misread this panel "movement" as a stretch, anytime welding is involved, you get shrinking as the weld cools.

On the panel fitment, you will likely find that any sharp 90 degree corners on a patch will help to add a bit of distortion. As your welds shrink, a tight inside corner gets those effects from two different directions, where the shrinking effects will compound in the inside corner, normally as a pucker that is a bit challenging to remove. On any corners of a patch, a large sweeping radius helps to balance out the shrinking effects on either side of the weld, where the planishing efforts don't need to focus on puckers or deformity on one side only. Where possible, limit your patch to a total horizontal seam so that these shrinking forces are more limited in amount by eliminating the number of perpendicular welds.

As to addressing the welds:

I have found that due to the manner in which each weld dot shrink pulls from ALL directions (MIG), you will have better luck in planishing to remove said shrinking effects if you can planish the weld dots while they are singular, sitting all by their lonesome. This will more effectively STRETCH that weld dot back out in all directions. And by stretching as you go, you help eliminate the panel being pulled into a valley on those long welds. As far as tacking the panel in place, (FYI) I normally would start the tacks at one end and work toward the other. I know many people will tell you to skip around to minimize heat buildup, and I have been one of those. But if you tack one end and then move to the opposite end, you run a greater risk that one panel may have more material than the other due to misalignment. Once things get all tacked up, this results in a panel bulge on one side of the weld. So tacking by starting from one end and working progressively to the other will help to eliminate this by being able to align the panels together as you go. Now that the panel is tacked and weld dots are spaced about (2 or 3"), go back and planish each weld dot individually, to add a bit of stretch. At this point, I use a 3" cutoff wheel to grind down the dots to just above flush. This gets them out of the way for planishing the next sets of dots, and by leaving them just above flush, you can do the final cleanup with a roloc sander all at once. By trying to grind things down to perfectly smooth after each, you run a greater risk of inadvertent sanding of the metal to the sides of the welds, which may thin and weaken the panel. So I hold off on this until the end. For your grinding disc, I prefer to use cutoff wheels about 1/16 thick. This gives a much smaller contact area than most any other method, so you will have less heat buildup from the grinding process. It also gives the best unobstructed view of what you're doing, so again, less chance of inadvertent abrading/thinning of the parent metal to the sides of the weld. Other grinding methods, such as using a flap disc, hide most of what you're doing, and generate too much heat. If you can't see what's grinding against the sheet metal, you're more apt to inadvertently hit it. Here is a link showing the grinding method on a plug weld, again, sanding on a weld seam I would wait until the end.

https://www.youtube.com/watch?v=V2WHT_zMOE8

Once these initial welds are planished and ground down just above surface, then continue, adding a weld between each one until your welds are spaced about 1" apart. At this point (still planishing and grinding after each time) instead of hitting the center between for weld location, start overlapping by about 1/3 of the last welds. By overlapping, you will have less risk of missed spots or pin holes. Continue with the weld, planish, grind, repeat until the seam is done. I typically weld from start to finish using weld dots only, none of the longer passes at the end, in order to keep everything consistent throughout the process.

For the cutoff wheels, I spend the extra coin and get ones rated for stainless steel. This makes them last longer and put less of that brown haze in the air that you see from the cheap HF or swap meet specials. By the time you figure out the cost of how quickly the cheap ones wear away, you haven't saved a thing. For the roloc sanding disc, the bulk of the welds are being removed by a cutoff wheel, we are only dressing what little remains of the weld and blending that into the parent metal. This is easily accomplished using a 60 or 80 grit, that should be as coarse as you need to go..