Yes the 6530c is a cat II and the plow does appears to be cat I, does the difference mean that the spare play between pin and link will cause too much movement, and result in a sloppy plow or damaged link?
YES
Plows have to be adjusted precisely. Unless the pins are bushed, to take up all the slack, you cannot adjust precisely and therefore you cannot plow.
The bigger issue is the 14.9" width of your Branson 6530 rear tires, relative to the furrow width of a 12" plow. I do not know any way to compensate for this.
It is possible your large rear tires will not fit deeply enough in the furrow left by a 12" plow for the plow to be properly adjusted. Tractordata.com specs Branson 6530 rear Ag tires @ 14.9-30. Industrial tires are wider than Ag tires. Are your tires flat in the bottom of the furrow, or wedged in above the bottom? In a perfect world your right side tires would be 6" below grade level.
My plow is an international, no manual for it.
If you start a thread in ATTACHMENTS seeking a manual for your International Plow, someone will likely respond with a web site where correct International Plow Manual is available gratis. Be careful to precisely identify your plow.
You mentioned adjusting the left to right adjustment by using the lifting rod on the three point hitch, my furrow has the crank on the horizontal offset pin shaft, what about that is it better to get that set in and just always use the lifting rod on the three point hitch?
The object is to have the plow level, when the tractor right wheels are 6" deep in a furrow. I have no experience with an adjusting crank on a moldboard plow but so long as the plow is level left-to-right after making the adjustment my guess is you will be fine adjusting either method.
I read an article on the web awhile ago that stated you want 18 hp per furrow blade, and you work them 1/3 of your moldboard size in depth, after reading that I thought i shouldn't use my 4220 because it was under the required horsepower and then I defaulted to my larger tractor, Is the 18 hp per blade true or should I be using my smaller tractor?
Branson 4220 has a Category I, Three Point Hitch and 12.4" rear tires so it is compatible with your Category I plow, which your Branson 6530 is not.
Tractor to plow considerations: horsepower, tractor weight, tire type, tire width, 2-WD Vs 4-WD, soil type, plow condition, plow size.
Branson has 42-hp and weighs (tractor only) 3,795 pounds. I trust you have 4-WD on the Branson 4220. You can pull a three bottom, 12" moldboard plow "no sweat" even through clay. For plowing, tractor weight and 4-WD are more important than tractor horsepower.
The parameters in which a 12" moldboard plow will properly turn soil: 5" to 7".
A 12" plow will move soil, but not flip it, pulled at other depths. Moldboard plows are not very flexible.
If you work a 12" plow just 4" in depth the furrow will be too narrow for your 12.4" right tires to roll 6" below grade level.