I've tried that same process before. It's more reliable if you flow some fresh SMD flux under the socket first as the remaining flux residue is often not enough to form a reliable joint.
The other problem is there's no way of telling if the joint has reflowed correctly as you cannot inspect the inner pins without X-ray equipment.
As you mentioned, it's important that no solder flows down the socket hole as it'd be near on impossible to extract it.
From my experience, the easiest and most reliable way is to completely remove the old socket using an SMD rework station, and use the individual pin sockets which come on a holder strip. The holder strip has the sockets at the correct spacing, so it's only a matter of lining the row up vertically and horizontally, soldering each of the pins by hand then remove the holder strip. Continue each row one by one.
The only tricky bit is keeping the spacing between rows perfect, but that's simple enough when using some miniture vernier calipers.
But it works well, and any bad solder joint is immediately obvious, as the socket pin would fall off :-)
