When I had mine blasted I used a company that had two booths. They hit it first with plastic media and then rolled it into the next booth with aluminum oxide, more aggressive, and only hit the spots that the media wouldn't take care of. This was done on a rotisserie so every square inch was stripped.
Once it is down to bare metal you want to get a couple of good coats of epoxy primer on it as soon as possible. I let mine sit a couple of days and ended up having to acid etch a few areas that developed some surface rust. Once it is sealed in epoxy primer then you can take all of the time you want for the metal work. Like zed240au said, just hit any spot you want to weld on with an angle grinder to take it back to bare metal and then when you're done just shoot that spot with epoxy primer to seal it back up.