I totally agree with your assessment of pressure washers... People think they are this magic machine that can clean anything... they can, but a scrub brush, approprite cleaning product and a hose is often quicker and better... and a lot quieter...
As far as your fridge leaking, there should be a drip pan in the bottom. Depending on the model, the plastic grill on the front at the bottom should pull right off (might have small screw or fasteners, but not usually) and you should see the plate. Some of my fridges over the years have had removable drip trays so you can clean them. See if the tray is full... it may indicate a bigger problem. You will often have a plate or part that heats up to evaporate the water that builds up. I think most of the water is supposed to be from condenser condensation so it may be indicative of an issue with your condenser.
I would:
1 - check the pan to see how much water is under there before rolling the fridge out. Get plenty of towels just in case.
2 - make sure your fridge and freezer are not so packed with stuff that the fans and vents in the back are blocked.
3 - Clean the coils on the back. THey build up with dust over time and cause the cooling system to work harder... BUT ONLY USE A VERY SOFT BRUSH, THEY ARE EASILY BENT AND DAMAGED!
4 - Check for any tubes coming off the back or bottom. THey may be blocked and overflowing something else.
5 - Take your wife to Lowes and buy her that new fridge she's been looking at...
