Hot air would be the easiest, I don't think a pre heater would be necessary.... gradually up the heat and don't focus on any one area... move in small inward moving circles... rinse and repeat until the solder flows.
Tip 1 is to apply fresh, 63 / 37 rosin core solder directly to the existing solder. Use a knife edge tip, and be generous with the flux. All you want to do is get the solder to wet and take in new solder. The new resulting allow will likely flow much better and easier than whatever was factory.
Tip 2 is to be generous with the flux, at all times. Clean metal and enough flux makes the solder almost "attract" to the joint where it should go, and seriously reduces the odds of a bridge unless you just use way too much solder
Tip 3 knife edge tip with temp controlled iron. I use a hakko 936 clone that I bought for $30 some several years ago. Bought a pack of knock off hako tips and have since had to replace the iron handle once. $50 all in or so, for well over 5 years of soldering on and off. A properly sized and shaped tip, as well as proper temp control... just essential parts of any beyond basic successful soldering job.
The parts will sit through or in through holes. So all you need to do is get the old part out (which should be doable with the setup I've described) and clean it up well with some desoldeirng braid. Again, lay down more than enough flux and with the knife edge tip simply lay the desoldering braid over the area and place the knife edge down on top of it.... use it to "mop" up the solder. It should wick into the solder easily. I've seen folks with bigger thicker braid stretch the braid a bit, and it seemed to make the capilary wicking action much better. Then when all the old solder is gone, simply insert the new jack and solder down one or two of the heavier pins with the knife edge, good solder, and lots of flux. Coat all the big pins in flux, then just heat and apply solder. Once it's tacked in place, you can do the same thing with the smaller pins. Cover libearlly in flux, tin the knife edge and just drag solder across all the pins on both sides. If you didn't overload the tip, you should wind up with perfectly soldered joints all nice and shiny with zero bridges.
Using these exact same methods, I soldered a micro HDMI port onto a board without magnification. The pitch width of the pins on that port was TINY.... so I did use a chisel tip for that, and not the knife edge... you could also try the conical tip... I just don't use it for much.
