Tried to get it all in the title:

How do I see my armor PERCENTAGE - using the console, of course - as opposed to this stupid number that's part of some large and ridiculous formula?

567 is 80% resistance, so that makes 100% about 709. So just do your armor rating devided by 709 and you will have a rough percentage.

There is an indice for "damageresist", but oddly this is always equal to your displayed armor rating (which is its own indice)

But the scaling isn't linear: http://www.uesp.net/wiki/Skyrim:Armor

Pfff thats silly. Then nevermind!

%DR is linear. What that graph displays is effective health. E.g., at 50%DR, you can take twice as much damage, so you have twice as much effective health. At 80%DR, you can take five times as much damage and have five times as much effective health.

But, each point of armor still contributes the same amount of %DR.

Yup, took a look at the displayed formula and you are correct, DR percentage scales linearly with AR.

I wanted to test the effect of a hidden GMST fArmorScalingFactor, so it would be relevant to see the actual percentage. Someone had to get the ratio somewhere.

Here you go.

fArmorBaseFactor = 0.03 ;This is the hidden damage resistance gained by equipping a piece of armor in integer form. Multiply by 100 for the %.
fArmorRatingBase = 1.00 ;This is the coefficient for the minimum effectiveness of armor, based on the skill.
fArmorRatingMax = 2.50 ;This is the coefficient for the maximum effectiveness of armor worn by an NPC, based on armor skill.
fArmorRatingPCMax = 1.40 ;This is the coefficient for the maximum effectiveness of armor worn by the PC, based on the armor skill.
fArmorScalingFactor = 0.12 ;This is the coefficient for the % damage reduction. Multiply by the displayed armor rating for %.
fMaxArmorRating = 80 ;This is the % maximum damage resistance from armor.


(armor rating + smithing improvements) * perks * ( fArmorRatingBase + ( ( fArmorRating(PC)Max-fArmorRatingBase ) * ( skill/100 ) ) )