Did some further research regarding Cow King drop mechanism. Again, thanks ZOMBY for providing me some links to these very useful information.
According to that here is an update to post
294:
Cow King's drops are divided into 3 scenarios
̶w̶i̶t̶h̶ ̶3̶3̶,̶3̶ ̶c̶h̶a̶n̶c̶e̶ ̶t̶o̶ ̶e̶a̶c̶h̶.Scenario 1: 60% chance to drop 1 rare item picked from Act4 "end game" item pool and one magic item from the regular (Act1) item pool.
Scenario 2: 30% chance to drop 1 unique item from Act4 "end game" item pool and one magic item from the regular (Act1) item pool.
Scenario 3: 10 chance to drop 1 set item from Act4 "end game" item pool and one magic item from the regular (Act1) item pool.For Scenario 2 if a failed item has been selected (exceptional one or the item already presents in the game as unique) another call will be made until a unique item drops or up to a maximum 5 unique calls (5x dura rares). This means that whenever an exeptional item is selected it is a default failed call and another call will be made. Also if you hoard certain uniques in your stash and inventory, you will have much bigger chane to control the drops. :D
Act 4 end game pool consists of the following items: Bone Helm, Crown ,Gothic Plate, Full Plate Mail, Light Plate, Ancient Armor, Gauntlets, Greaves, Plated Belt, Gothic Shield, War Scythe, Pike, War Sword, War Staff, Great Sword, Long War Bow, Giant Axe, Great Maul, War Hammer, Flamberge, Mask, Repeating Crossbow, Ring, Amulet (only seen magical ones so far) and probably a few more. Of course in NM and Hell the exeptional types of the above mentioned items also can be dropped, with the exception of Lance and Grim Helm (due to an item generation bug, these items can not spawn).
What I did not know until now, is that all Scenarios share the same patterns.So it is based on the actual seed that Cow King will drop e.g. War Axe on a certain spot.
In Scenario 2, if unique version of War Axe is already in the game, another item will drop, always the same according to the seed e.g. War Bow. And if the unique version of War Bow is also in the game, the third item comes and so on.
So Cow King drops in patters, and based on the map seed, position of CK and your way of killing him, you can expect a limited number of patterns.This means that if you hunt for Rings and Ornates, you shall search for maps which have drop patterns containing these items. Also you do not have to keep all the unique stuff at your character, if the map have no Great Maul pattern for example.
But for example if you keep a War Axe in your stash it can force a War Axe - Ring - Ornate - Ring - Ornate pattern (dont know if it exists, just an example).
For more info you can search for
"Treeharls 1.00 Cow King running guide".Based on the information above I started to search for maps with Ring patterns.
This map for had potential for Ornate (see my dupe post above) and Ring. I made like a hundred runs, on that map. Unfortunately no epic drops, only this Ring woths showing:
https://i.imgur.com/QUjXUon.jpgPerfect light res, life leech and only lvl18 requirement. Imagine that with an additional 15 all res affix. :)