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I just wanted to report back for anyone that needs the help. I replaced the heater core last weekend and solved the problem. There was a puddle of coolant in my box and the core was certainly leaking.
I bought my core at Napa and although it was squared off on the top and bottom (unlike my original unit), it fit like a glove. The only problem I have now is when I turn the fan speed on high, I get a slight whistling sound that is annoying as can be. I suspect I need to put some new seam sealant around the area where the heater core spouts stick through the firewall, as there was a good bit there to begin with. Otherwise, I now have great heat again, with crystal clear glass.
It is very easy on a A/C truck, too easy you say to yourself after you have completed the job. There have been some threads where people have had trouble making the aftermarket heater cores fit though. Just keep an eye out for that.
I have to say, I actually did say "that was way too easy" to myself, and then I remembered your post. I kept checking to make sure I didn't miss something...LOL. Usually Ford makes repair work a little more challenging than that!