Cleaning dirt out of heater core box

Lowe's usually has the coil cleaner..

 

First, you're talking about air flow - fan blowing across/thru core fins, not fluid flow inside, correct?

For the air flow:
Heater core is just a little radiator; can't you take an air hose and blow thru it? (Wear a dust mask.)
Sure, you're gonna make a mess, just cover your stuff w/giant garbage bags,
cut them and duct tape if you have to, but most is fine road dirt that we get into anyway, nothing toxic.
I did something similar when I changed my cabin filter and found all kinds of crap in there.
I took one of those giant 3 foot fans, on high, and opened both doors to minimize what settled in my cab.
Not too bad, also periodically blow hose around inside - often - to keep crap from settling inside. You can add a shop vac near the exit to capture more of the mess, too.
I think if you wet it - it will just be harder to get out. JMHO.
Then you can Armor-all the stuff you were meaning to clean in there anyway from winter.

 

I would take the air cleaner out and use a vacuum on it. I would not use water while still in truck, There is no way from preventing water from getting inside truck. If you want to use water I would use 2 hose pinching pliers to pinch off the heater hoses and remove the heater coil and clean it very good with water, outside of the truck. The foam cleaner I use comes from a plumbing, heater and A/C supply house, the foaming stuff is very strong acid based. They sell a green one that is not acid based but does not foam as much.

 

Whether you blow it out or rinse it out go in the opposite direction of the air flow so that you are pushing the dirt back out instead in. there is a drain in the bottom of the box, if you think it is plugged open the hood, find it and clean it out.

 

How accessible is it from outside the truck? Is there room to maneuver?
I do like Expeditor's idea of the hose pliers - to pinch hoses off and totally remove.
Then I would just blow it out with shop air.

 

Only takes a minute to pull the cover and look