The only time I have worried over the stain was when I extended the transoms and needed to get a good color match. I then let the stain come back. As far As I'm concerned, worrying over the mustache is like washing the bottoms of your shoes. That said, I used very dilute CLR (probably less than $1 worth) in a spray bottle. Worked fast.
1. Acids do not just very in pKA and pH, they also vary in their relative aggressiveness towards metals. For example, for a given amount of scale removal, vinegar will cause more metal damage than anything else. I didn't test lemon juice, but I would expected it to me more like CLR (lactic acid). For iron, phosphoric or HCl (properly diluted) will do the least damage. For aluminum, CLR is probably the best. Thus, the best choice depends on the metals at risk. I recently did some tests for a magazine.
2. Gels just increase contact time. Soaking a rag the solution and leaving it there does the same thing. MSDS/SDS data will tell you which acid they use.