[VRM]

Get some radiator cleaner or CLR and set up a closed system consisting of the heater core, and the hoses disconnected from the block. You may want to get some longer hoses (I have a couple of 5 footers that I use) and some clamps and some plastic or nylon spigots.
Drain the coolant from the core, and then fill with the cleaner following the directions (I prefer a stronger mix of cleaner). Let it sit for a half hour or so, and then drain into a bucket - this stuff is a mild acid, so be careful with it. Then use your garden hose to blow out the loosened gunk - keep forcing water through until it comes out clear.

I've been told that Ford products have their cores buried in the dash - my old Blazer had it behind a panel in the firewall - really easy to get to. They are easy to replace if it does not clean out properly, but you may have to take apart the entire dash assembly.

You guys need heaters in Alabama?!?

Steve