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I swapped a bigger radiator into an 83 F-150 with a 300-6 I had. It was a radiator for a V-8 I believe and it fit just fine. Every truck I've seen had the provision for a bigger radiator, you just have to move the mounting pads outboard to make it fit.
The Radiator supports are different for 300 I6's with standard cool and Extra cool, than the ones for Super cool and/or air conditioning. A Super cool Radiator will bolt right up however, just place the mounting brackets in the wider location holes provided. You will need to change the upper radiator hose to one for air conditioning or super cooling.
The difference in the supports is the hole that is in the radiator support for the radiator. The one for standard cool has a smaller hole the size of the smaller radiator, and the super cool has the wider hole like the V8's. If you put a super cool radiator in a standard cool radiator support, the hole difference will block off or restrict air going through the larger portion of the radiator etc... To get the full benefit of a larger radiator, IMO, I would switch the radiator supports with one with a bigger "hole" for the larger radiator.
To finish off the job, I would replace the fan guard with a fan shroud that will fit on the super cool radiator, and install a fan clutch if one isn't already installed for the maximum of cooling you can get.
A great radiator for the Inline six is a GM crossflow from the 70's - 80's midsized rear drive V8 cars. Get one from a salvage yard and get the brackets that go with it. Easy to swap in, the hoses have the proper locations.
Of course the others options posted above a just fine too.