Jordan
In this case a stick welder isn't really what you want. It may suffice if you use very thin rods and turn you amperage right down.
I'd firstly prepare the new patch getting it as close as possible to the original shape that you cut from the panel. You should try and take out any of the dents and dings in that panel that you want to get rid of.
Where the panel was originally attached to the angle-iron by spot welds, if you don't want to have visible welds, one method is to drill a hole with the same outside diameter as the spot welds and weld a small rosette weld in the hole attaching your panel at the same time, then finishing by filling the hole again.
So, my advice would be to make your new piece paying attention to match the edges to the remaining original panel and take it to the nearest panel shop and have a welder there do the hard part for you. To be on the safe side prepare two replacement pieces just incase the welder burns holes in the first.
From there you can take the finished job home to work on removing the obvious welds with your grinder - but don't get too excited or push too hard as you don't want to make any new dings or cuts and scratches. If you can do the job by hand in this case it's much better. Its harder to make a stuff up if you are filing or sanding by hand than it is to bugger the whole job with your grinder.
Anyway that's my advice
But keep up the good work champ.
Pedr