Does anyone have experience with a reciprocating air saw who could tell me how this tool could be expected to perform in this situation[/QUOTE]
I own a couple of each (one is a Mil cough cough waukee) and use them all the time . The Milwaukee is actually my favorite- they make excellent tools. As stated, the air saw is too fast and will EAT blades. The Sawzall would be my 1st. choice because it is slower-variable speed actually. Get the best blades you can buy. I actually cut 1/8 thick metal 1 time with a Bosch Skill saw (guess that's what you call it) with a course wood blade!!! I had 5 holes about 4" by 5" to cut. The fellow at work that loaned me his saw gave a new wood blade and when I told him I couldn't cut metal (much less 1/8") with that he said sure- go ahead. I thought he was NUTS! I cut all 5 holes with that blade and didn't even dull it that much! If I hadn't done it I would NOT have believed it. Stainless is a different animal though and I can't say how well it will cut but I would still use the Sawzall. I don't think you've known frustration until you've tried to cut 100- 200 stainless bolts with an air saw.
LOL Good Luck