The crud in the radiator doesn't look like oil to me, more like cooling passage debris. Changing a head gasket is FAR easier than replacing the rocker oil tube. If you decide/need to replace it the procedure is outlined in the Shop Manual.

Crud removed does not look like oil to me either. If oil it should spread out to the paper towel quickly. Like the oil ring under the dip stick. So should water. If fiber or solid it will not leave a ring on the towel. I think the owner should do a clear water flush until the crud is removed and then see what results when the engine is run for a short period of time.

If the coolant and oil are mixing then the oil will look like a milkshake.  Drain the oil and see if it resembles a milkshake.  If that motor has not been flushed in a long time that might be rust and other contaminants.  I agree with above to try flushing it and see what happens.  

Thank you gents now that you all mention it, it reminds me that you all suggested that last time. I think I like doing things the hard way. I suspect the engine has not been flushed in a long time. I did install a new radiator too. I will flush the radiator and engine this time and check afterwards. I assumed(not a good idea) that the junk in the radiator was oil as it was clean prior to restarting after a year passed. A new radiator and sitting for over a year might have introduced some contaminants to the system which would be a pleasant surprise. I will get on this very soon as I want to putt around town this season

Having never flushed a cooling system any suggestions flushing coolant system without coolant going down the drain? I live in California so we can’t allow antifreeze down the drain, it’s toxic.  

Good point. This might be the time to let a professional do it. I assume there is equipment available that can do a full recovery flush but it's likely expensive so, as expensive as having a pro do the job is likely to be, it's probably cheaper to farm the job out than buying the equipment yourself for a one time job.