I'm looking on some ideas on how to gear most efficiently as a tank. This is beyond the standard "STA > all". Not really interested in arguing something like that without context. What I'm more interested in is discussing how to get the best deal.

Enchants vs. Gems/Food

For enchants you tend to see a 1/1 ratio (or worse) of stats/STA. Yet with foods and gems the ratio is 1/1.5. Provided you are seeking a balance of stats, then you should avoid STA in enchants and go for things such as +6 all to chest, +12 def to bracers, +12 AGI to boots. You can then take STA when it is a "better deal" elsewhere.

Battle Shout vs. Commanding Shout

BS = 305 AP ~= 152.5 STR
CS = 1080 health ~= 108 STA
Here it is flipped with about a 1.5/1 ratio compared to gems. Generally, it wouldn't make too much sense to socket/enchant STR to up your aggro and then use commanding shout over BS.

AGI vs. crit/dodge

It is more efficient to replace avoidance with AGI than with crit if you are looking to boost aggro. In rough terms it takes about 20 crit and 20 dodge to get the same effect as about 30 AGI if you again use gems as a baseline (not to mention the slight armor bonus).

STR/AP vs. Block value

This is a bit rough so you may want to correct me -
7 STR = 14 AP = 1 DPS
1 block value = 1.3 (shield spec) damage on shield slam every 6 seconds
6 block value = 1.3 DPS
(1H spec left out because it applies to both)
This does not take into account the specials that STR applies to, the 1/20 block val per point of STR, or the rage generated by white damage. But it does tend to point to 1 block value > 1 STR while with itemization it appears that 1 STR costs more than 1 block value (look at autoblocker vs. bloodlust brooch). Also, based on this I'd look into getting an "aggro shield" with +18 block value instead of +18 STA (ie azure shield vs. shatar exalted).

Socket Bonuses

+XYZ to dodge, hit, etc. socket bonuses do add up. It is not difficult and is less expensive to buy green and purple gems rather than solid stars.

Specialization

I'm leveling engineering not only for the helm next patch but also for the +45 STA trinkets to be able to swap in an 900 HP when needed. It is preferrable to have highly specialized pieces of gear to swap in to boost whatever stats you need. Unfortunately, more specialized pieces seem to suffer from some kind of itemize penalty.

Talents

I haven't done this analysis yet but I would be interested to see how cruelty, anticipation, toughness, 1H spec, vitality, and any other talents translate into itemization.

Well, anyhow ideas or feedback would be appreciated. I'm sure I must've messed up some equations or algebra somewhere along the line.

Yes, in a fight where avoidance is not as important other stats, you might wish to forgo the avoidance of defense but maintain crit immunity. In that case, resilience is 1.5 times as effective as defense for becoming crit immune. In particular, I'd take a look at the 2 piece PVP set bonus for 35 more res. Take the shoulders and chest for example, both have the highest amount of stamina out of any blue gear for their slots and the same amount of sockets.

Also, I remember someone posting somewhere that their enrage proc'ed even though they weren't crit while wearing resilience. Makes you wonder if there could ever be a niche for a more fury based tank in a scenario where aggro is empasized over survival.