Since you're working with already once-wetted surfaces, try some good no-clean flux. It's not as aggressive as the highly activated or RA fluxes. I get mine in syringes as a liquid (not the paste flux, but I have that too).
On a whim, I bought an inexpensive hot-air rework station (an Aoyue). I found that my first attempts proved that I needed practice, but after a few components, I got the hang of it. (I'm not suggesting you go out and buy one of these, but if you get into enough SMD rework, you might consider it.)
Images below are of a lighting board in a model RR car... the first (Image 9) is the manufacturer's installed LED and questionable soldering work. The second, (Image 10) is my replacement of a similar LED using hot air.