Removing rosin flux residue from PCB
I bought some boards from these guys a while back and had similar issues (you just really want to show off the pretty boards).
I very successfully cleaned them by first using a lot of isopropyl alcohol with a trimmed down paint brush (so it's more firm for scrubbing). Then before it evaporates, and I know this sounds crazy, rinse it really well with deionized (DI) water.
You've probably noticed that when you clean with isopropyl alcohol they look great until they dry. The water flushes all that away and it drys clean.
Give it a good amount of time to dry and blow out the underside of the ICs with compressed air. I had quite a few ICs, LEDs, FETs, other discretes, and even an LCD on that board and all three boards that I put together worked perfectly and looked fantastic.
At the hobbyist level, a high concentration rubbing alcohol (the stuff I use is 92% and can be acquired at Walmart) and an acid brush will suffice. If you're really frugal, an old toothbrush will work if you clean it first.
Mass produced boards typically use a reflow soldering process. The amount of solder paste is carefully controlled and consistent from board to board. If the board comes out very clean and pretty, the paste used was most likely a variety that contains no clean flux, as opposted to rosin core flux.
Isopropyl alcohol works, but what REALLY works is ethanol. Dedicated flux removing chemicals are mostly ethanol and just make the flux disappear. All you have to do is look at the composition of a bottle of flux...the solvent used is ethanol.
Mechanical action is only really required to disperse the dissolved flux, not to scrub through solidified flux. If I just soldered the board, I literally just have to dunk it in an ethanol bath gently swish the PCB around to agitate things a bit, and tip it as I take it out. If I leave it for a week after soldering so the flux thickens, then I just have to leave it submerged for longer and maybe lightly brush it a bit before removing it from the bath.
They are also $60+ a jug, I assume because it's mostly ethanol which is drinkable.