Mike,
Reverse flow of the heater core can be done with a gallon jug of hot tap water. This will tell you a lot.
1. Remove both hoses from the heater core.
2. connect a short hose and funnel to one side of the heater core.
3. pour the hot water ( the hot water you get out of the tap is fine ) into the funnel.
Now look at what happens.
4. if the water drains from the funnel and no water comes from the other end, you have a leaky heater core.
5. if the water drains from the funnel and come out the other end, look at the condition of the water. Lots of gunk means you are cleaning it out.
6. if the water does not drain from the funnel, the heater core is plugged.
So, you put a gallon of water through. Now do the other side.
You should switch back and forth until you can get water flowing both ways.
If the heater core is plugged. You can use 15 PSI of compressed air to force blockages out of the core. Be very careful, pop the core and you will not be happy. To do this, place a rubber hose that fits inside the heater core nipple. Scale the opening down until you can fit an air nozzle into the nipple without it leaking. Then you will need to an inner tube. Fill it until it reads 15 PSI. Stick the fitting of the inner tube into the opening you just made and let the ait escape.
This works sometimes.
Hope this helps!!