Edit - 3-30-13 - Alright, I hadn't updated this in well over a year. A bunch of stuff has changed, let me know if I need anything...

General: 1x Braids, Conjurer Adept

Creature (19)

1x Arcanis the Omnipotent
1x Braids, Conjurer Adept
1x Consecrated Sphinx
1x Descendant of Soramaro
1x Diluvian Primordial
1x Ixidron
1x Jin-Gitaxias, Core Augur
1x Jushi Apprentice
1x Kami of the Crescent Moon
1x Lighthouse Chronologist
1x Patron of the Moon
1x Phyrexian Ingester
1x Phyrexian Metamorph
1x Rimewind Cryomancer
1x Roil Elemental
1x Sphinx of Magosi
1x Tidespout Tyrant
1x Tomorrow, Azami's Familiar
1x Trinket Mage

Artifact (11)

1x Caged Sun
1x Extraplanar Lens
1x Library of Leng
1x Planar Portal
1x Proteus Staff
1x Sapphire Medallion
1x Scroll Rack
1x Sculpting Steel
1x Sensei's Divining Top
1x Sol Ring
1x Temple Bell

Enchantment (7)

1x Land Equilibrium
1x Leyline of Anticipation
1x Omniscience
1x Paradox Haze
1x Rhystic Study
1x Telepathy
1x Thought Reflection

Sorcery (15)

1x Ancestral Vision
1x Beacon of Tomorrows
1x Call to Mind
1x Fabricate
1x Inundate
1x Mystic Speculation
1x Recurring Insight
1x Relearn
1x Rite of Replication
1x Rush of Knowledge
1x Stolen Identity
1x Time Stretch
1x Time Warp
1x Trade Secrets
1x Wash Out

Instant (13)

1x Blue Sun's Zenith
1x Capsize
1x Cyclonic Rift
1x Forbid
1x High Tide
1x Last Word
1x Long-Term Plans
1x Mystical Tutor
1x Pact of Negation
1x Rewind
1x Spell Burst
1x Spell Crumple
1x Time Stop

Land (34)

1x Academy Ruins
1x Halimar Depths
1x Lonely Sandbar
1x Reliquary Tower
1x Scrying Sheets
28x Snow-Covered Island
1x Tolaria West

Planeswalker (1)

1x Jace, Memory Adept

My first deck was Blue Braids, and I played Archmage Ascension just like you. I have bad experiences with it, always wishing it was another card. There were games that I'd get it active, but that was the turn I'd either win or lose on. It was never active when it meant something. I really recommend you change it to something mroe beneficial to the deck.

Looking over more of your list, I'd tell you to keep the Braids targets to about 10-15. Your deck is supposed to win off the back of your general, and off the back of almost 1 creature at any given time. I played before Emrakul was banned and it was great to land turn 3 (ala Sol Ring turn 1).
So that said, you should probably choose a number of Braids targets and cut some of the rest for support creatures/draw effects. That was always a good part of playing this deck. Running support wizards and cards that interacted (lookin' at you Azami!) was always good.

My original build had a ton of proliferate effects, but the Archmage Ascension was just as much of a dead card as you wrote.
The only reason it's back in there is for the synergy with Consecrated Sphinx. In a match the other day, I played it early and it had 3 counters when I played the Sphinx. It went active before they could blow the Ascension (which they did after I pulled 4 cards with it), and I finished the table with a sweet Psychosis Crawler + Blue Sun's Zenith.

I'll think about reducing the Braids targets for more utility, but I kind of like the unpredictability at this point.

Of course "fun" is totally subjective to each person but I don't think cards like Mindslaver are that much fun to most EDH playgroups I've met...

How about adding some more big/splashy type effects that spice up the game?

Off the top of my head.... Day of the Dragons, Mass Polymorph, Eye of the Storm, Blatant Thievery(Don't expect to live too long after casting that last one!!)

When I played Braids, my initial experience was Braids dying before I got anything for free. My deck consisted of these types of cards.
1. Big stuff to Braids in
2. Stuff to accelerate to 6 mana on turn 4
3. Stuff to protect Braids. Generally, I didn't consider it very useful unless it could protect a Braids with 2 mana backup.
4. Card draw
5. Random good stuff / sweepers

If you cast Braids on turn 4, and you want to have at least 2 "good" things in hand to cheat out, then you will need at least 18 Braids targets. The trick with the "Big Stuff" is to make it serve double duty as a sweeper, card draw, or as a way to protect Braids.

New edit posted.

Try Kira Great Glass Spinner to help protect Braids.

Gilded Drake lets you capitalize on opponents bombs.
Memnarch does wonders too.

Ulamog provides much needed removal for mono-blue. Also annihilator helps control the free permaments from Braids' effect.

Repeatable bounce effects like Linessa, Time Elemental, Equilibrium and Capsize should help stabilize the tempo engine. Nonetheless Blue Braids makes for some quick, swingy, and memorable games,

I recently got a Blue Braids and am also wanting to have her command one of my decks. One of my favorite Blue cards is Vodalian Illusionist. I figure I can phase Braids out on my turn so nobody else gets her benefits. The Illusionist also doubles for defense. If some big targetable fatty attacks, I just phase it out. Or if one of my more precious critters is about to go bye bye, I'll phase it out before the board wipe or doom blade happens...

That is a good idea, and I do run Vanishing. I find that typically I want the political upside of allowing my opponents to play their stuff, but it is good to at least have that threat.

Updated - 3-30-13

It seems like Kami of the Crescent Moon and Temple Bell would suck something horrible in this deck. I mean, giving others cards when they get one free permanent a turn seems REALLY bad. If this isn't the case, I would be very curious as to why.

My buddy had a Braids deck a good while ago. Some cards he liked:
-Every Eldrazi there is. Even the common ones did fine until he could pull the money for the big boys.
-Duplicant
-Contagion Engine: Seems weird but it works.
-Great Whale: he ran Palinchron as well because combos, but getting an extra 7 mana from this guy isn't a bad deal either

The reason the deck works is the political aspect of the game. Once Braids is out, all you're really looking for is for the other players to balance each other out. So if multiple people are dropping stupid things into play, they have to focus on each other. That lets me gather cards until I can go nuclear.

So one of the big priorities is to not draw too much attention. Unless you have the line of play I had the last time I played it.

Turn 1: Land, suspend Ancestral Vision
Turn 2: Land, Howling Mine
Turn 3: Land, Paradox Haze
Turn 4: Land, Braids, Conjurer Adept
Turn 5: Ancestral vision resolves, 2 triggers = Caged Sun, Jin-Gitaxias - Cast Time Stretch

Yeah, no one else got a turn after that.