Electrical – Use potting compound to secure solder joint

Ideally, you should avoid finding yourself in this situation. Using appropriate connectors or atleast making sure you have enough room to comfortably attach the wires on the pads is a useful thing to do. You should certainly try to fix the problem more robustly if you want to produce or manufacture the thing.

For a one off thing, though, hot glue should work. There is a technique called potting, which using a different material, which does essentially what you imagine hot glue will do. Typically, potting is used to reduce stress at connector/solder joints and prevent cables from flapping around and so on. The potting material is better at doing this if the signals are especially sensitive in some way, since hot glue isn't a material explicitly chosen for it's insulating/dielectric properties. You should give it a go, though, for most applications it's probably insulating enough.

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)