I'm not a professional welder, but have taken classes and just got done welding in 1/2 of a firewall and 1/2 an inner fender panel and fabricating part of a battery tray and welding it in. I could weld about 2 feet in 10 minutes skipping around to keep the heat down.
I haven't had your problem so I will tell you how I did my welding and smoothing in the hope that your process will go faster and with better results.
I use Harris Twenty Gauge wire. This has to be used with gas, but has a powdered metal core. This is the easiest wire I have used on sheet metal, but I try to always have a piece of flattened copper behind what I am welding held by a magnet to act as a heat sink - once again to minimize heat buildup and in some cases to actually keep the patch in position - nothing like killing two birds w/one stone!
If I didn't have to reposition this piece of copper I could weld faster maybe - but then I also might be more afraid of burn through and maybe not get penetration, but I really don't think lack of penetration is a problem with sheet metal...
I really don't like using a grinder on sheet metal - used it plenty when building my rotisserie, so I use cut off wheels and flapper disks as suggested already.
No big secrets except for maybe the Harris wire.
Hope this helps.