It never happened to me that converting to sRGB would be a better option than converting into the monitor profile. If you want to have your photos correctly diplayed on a monitor, you have to convert into that device's profile. The problem is that there are as many monitor profiles as there are monitors. Thus far, I obtained better results by converting into my monitor's profile than by converting into sRGS. Maybe is my monitor the universal one.... If you have the time, you can convert into sRGB, give it 10 iterations, as suggested above, until you are satisfied; how much do you trust your eyes???