That's a Card Captor Sakura pic. 
Have a cookie.
So after spending some time pondering and reavaluating, Ive decided to nerf down Spell Attuned.
You are right, it is much to powerful as is. I was under estimating how much more effective an option it was compared to the other abilities avaliable. It was to easy to get fullcasting with it as it was, and made taking a spellcasting dip beforehand almost mandatory because of how effective it was.
I was a little biased with it because I really like Gish classes and was giving a bit too much focus on the rule of cool over balance in regard to the ability.
Anyways, here is the nerfed ability:
Spell Attuned: Select one arcane spellcasting class. The Elder Eidolon gains new spells per day and an increase in caster level (and spells known, if applicable) as if it had also gained 1 level in an arcane spellcasting class to which it belonged before adding gaining this geometry. It does not, however, gain any other benefit a character of that class would have gained. If it had more than one arcane spellcasting class before becoming an abjurant champion, the elder eidolon must decide to which class to add each level for the purpose of determining spells per day, caster level, and spells known.
An Elder Eidolon can select this ability more than once, increasing spells per day and caster level for one arcane class as if he had gained one level in a spellcasting class. This ability can only be taken a number of times equal to the class level of the Elder Eidolon.[/li][/list]
It is only +1 Casting each time. As a Mental Geometry you can normally only take it 6 times over the 10 levels, barring spending 4 of your 7 feats into the Mixed Geometry feat and losing a lot more geometires. And if a character goes that option, they can't use it to get Mystic Therge style progression do to a cap on the amount of times you could take it.
I think this should be better but Im not 100%, so let me know if it needs more tweaking/nerfing.
Ok, let's have a quick recap of what this class gives:
-6 mental geometries.
-10 physical geometries.
-A total of +6 Str, +4 Dex, +4 Cha.
-Construct goodies and d10 HD.
Each physical geometry is easily equal if not better than a feat, so assuming you "burn" 4 feats on Mixed geometry, this class can grant:
-10/10 fullcasting advancement.
-2 "free" physical geometries (4 swapped for spellcasting, another 4 to make up for the feats spent in Mixed Geometry)
-A total of +6 Str, +4 Dex, +4 Cha.
-Construct (or living construct or plant) goodies and d10 HD.
Note also that many fullcaster prcs do force you to burn some feats to enter as a prerequisite.
It still seems like fullcaster++++ to me. This blows out of the water basically every official gish prc I can think of like Abjurant Champion (that is mentioned in your text and everything) and whatnot.
A simple nerf though would be limiting the number of times you can take that mental geometry to 1/2 or 3/4 your Elder Eidolon level, so you're always one or more levels behind an actual fullcaster. Which is basically what gishes are supposed to be. Sacrifice some magic for melee prowess. In particular because you seem to be forgetting this is supposed to be an almost mindless melee-smash monster, so it just doesn't make much sense that the best thing the class does is being a 10/10 fullcaster prc.
On modular design: It needs better wording. The way it's written now you're basically gaining two extra designs, only one is active at a time yes, but still one extra design per feat. I believe what you mean is something along:"Choose one of the physical or mental geometries you currently possess. Choose another of the same kind you don't have yet. As a standard action you can swap between them."
