Firstly your spark plug sounds like a rather cold heat range. If you want to stick with a Champion plug I would recommend trying a RF11YC or a more likely a RF14YC. Those are the next two steps hotter in plugs that Champion makes. I ran some really cold plugs on a high compression Ford before to avoid preignition caused by spark plugs getting too hot. I ran the RF11YC and then moved to RF9YC. They fouled easily but let me run pump gas. Even when the car was stock I tried Champion RF18YC plugs (recommended heat range for teh motor) and they fouled more easily than other plugs I've used.
Since then I stick with Autolite spark plugs in my Ford motors. Personally if it were me I'd start with a set of trusty Autolite 45 and take it from there. Get the engines up to temperate and go for a short cruise (be sure to get on it a bit though) then pull a couple plugs and see what the heat range looks like.
You can tell if the heat range is too hot or cold by checking where the discoloration on the ground electrode stops. It should stop right about in the middle of the bend in the ground electrode. If it's more towards the threads then you have a plug too hot for your motor, so go colder and try from there. If the discoloration stops before it gets to the bend in the ground electrode (more toward where the tip of the ground electrode is nearest the center electrode) then you need a hotter plug. Unfortunately since your plugs are so badly fouled I can't tell fomr looknig at them what the heat range is like. I will say that as far as Champion plugs go a RF10C sounds rather cold for a stockish FE, which can contribute to fouling.
Your plugs fouling are most likely from too rich a mixture. Air entering from worn throttle shafts is a possibility, as someone else mentioned. It will however NOT cause a rich condition. It will in fact lean the mixture as fuel is added to the air stream upwards of the throttle shaft bushings. You will typically get a lean idle and low RPM operation (doesn't affect high RPM nearly as much). Your idle speed may be arratic, sometimes slightly higher or lower depending on if your throttle shaft vacuum leak is erratic or if they are worn enough to leak constantly. If it is a very bad leak you may get a slight surging at idle and off-idle.
One easy thing to check to see if your carbs are giving you trouble in the source of a rich situation (despite adjustment) is to run the engines up to temperature and shut them off (do not pump throttle before shutting them off, just let them idle for a minute or so and shut them off). Then go look down each venturi at your throttle blades (use a flashlight). If any of the throttle blades look at all wet you have found the source of your over-rich problem. This type of problem is most often caused by boiling/hot fuel. Other typical causes include worn or dirty needle and seats, sunken floats, or things of that nature (basically anything that can cause an overly high fuel level in the bowls).
