The way I've always done it is take filter off, pull block heater. Take a shower in the antifreeze that comes out. Remove bolts. Front I usually take the tire off and come through wheel well with some extensions. Pull aseambly out torwards transmission. Get a rubber maleate and hit ends off. Replace orings, grease! I use a press because I'm a scrony feller and don't have enough lead in my a$$ to get the caps back on. Getting the cooler back up in can be a pain. Make sure you don't have your tongue over your eye tooth. It'll go in. Replace the gaskets. I put the front two bolts in first. The assembly should spin to catch the back 3. Torque specs are 18 ft lbs I believe. Teflon tape on block heater. Replace or put filter back on. Add coolant and oil as needed.
That's how I've always done it. Never had oil in antifreeze or vise versa and I've done 4 of them.
Also make sure they're ford orings. Diesel oring has them for 75$ or so.