(This is a trick we use to make the job better, give it a try)
You noticed I did not say “easy”. Working with a 25+ year old war horse like ours is rarely called “easy” but it’s not rocket science so we just can’t help but try & do things in the back yard that should have been taken to a shop to get done. Here is one and let me help you a minute to do a better job than before.
Your radiator sits up there in the front behind the grill never saying a word. Every now & then you take a look at it and find no leaks and figure it’s OK and that may be your first mistake. This radiator core was not leaking 
but with over 30% of the core clogged it was not flowing very well either! The problem was the fan clutch was staying on constantly and it would to offset the lower cooling capacity of the clogged radiator. Everything else was
checked out & good in the system so the finger pointed to the only other component- the radiator. Now the system should work properly with the new 14 fin per inch, 4 tube high efficiency radiator, hey but this is not where I can help you. You should take for granted that the radiator needs help if it has any age at all on it and there is a cooling issue.