Removing solder effectively

The problem you are facing is that 30W can't produce enough heat to melt solder that is in contact with a lot of metal and consequently works as a heatsink.

Best option is to buy a temperature controlled soldering iron that has a higher wattage, the advantage of that is it can reheat the tip very fast when it detects that the temperature is dropping by providing 50w or 70W or even more (depends on the model).

The cheap alternative is the heat gun which is powerful enough to melt the solder but has no temperature control so it's up to you to control the applied heat.

My suggestion if you intend to use the heat gun is to put some solder paste (avoid inhaling the fumes) on the solder you want to remove which will help it melt when heated, place a desolder braid over the solder and heat it with the gun from the opposite side (The order is I mean is in layers from bottom to top : solder / paste / braid / soldering iron , in a sandwich fashion). This way you will be able to remove the solder little by little without overheating too much the surroundings by sucking the solder in the braid as soon as it melts .

Finally there is always the despair solution which is to cut the wires as close to the end as you can and resolder them to the new plug (assuming they are long enough)

You do need a bigger iron, but I too would be nervous about going for the gun - they aren't temp controlled and tend to make a mess of things if you aren't extremely careful.

See if you can find a friend with an iron with higher output and temperature control - that's what you really need. Alternately, you can buy a better iron. If you do, make sure to get something with temperature control and 50-70W of output.

The tip on the iron will make a difference; to tranfer lots of heat, you need a nice, wide tip. If you're using quite a pointy tip, try swapping it for a chisel-type tip (or similar).

Another option might be to try desolder braid (or some stranded copper wire) to remove the solder in preference to the solder sucker.

Personally, I'de be tempted to try the solder gun, but while taking care not to over-cook things. Do it in short bursts and let things cool off a while in between if necessary.