Well, that is an easier fix than your firewall or even a seam...just replace the heater core...check that the hoses are clamped properly first because it could be backspraying around the hose and dripping in from there...but if that is not the case, removing and replacing the core is the only fix I'd recommend...they are fairly inexpensive and take about 20 minutes to replace even if you've never done it before...
Just remove the clamps from the outside firewall, undo the screws that hold the panel over the heater core, and pull it out...pop in the new one and something to keep it from wobbling around if the replacement doesn't provide this...then connect the hoses and clamp them on tight...then top up the fluids...
Total cost should be less than $40 even if you have to buy new hoses and fluids...