Those IC sockets look well past their best! Some high-quality turned-pin replacements will make a world of improvement.
Look upon it not as hours of tedious work alternately priming and firing a desoldering pump, but as an opportunity to treat yourself to that vacuum desoldering station you have always wanted ..... Available from the same sorts of places you'd have to go anyway for a reel of solder braid and a flux pen that you probably would need to help things along if you were determined to do the job by hand, so it can't hurt just to have a quick peek before you hit the checkout
