I see two problems here.
The first is that you are trying to run a mono-blue group-hug deck in a format where the general consensus is "Mono-blue must die!"
The second is that the things you are dropping with Braids just really aren't that great compared to the things that your opponents will probably drop. I know it's monocolor and your options are limited, but if you don't put up a big scary wall, the one opponent who wises up to your tricks out of the five at the table is going to stomp you as soon as you try to get started.
Suggestions by category:
GROUP HUG:
Actually, I like this suite. I would suggest
Blue Sun's Zenith for reusable politics and
Prosperity in addition to what you have. If you wanted to be really mean, you could add
Pact of Negation for
Hive Mind, but that's up to you.
DRAW:
Your spells are solid, but some of your permanents in this category could be better.
Azure Mage is playable, but there are better options.
Oculus,
Runewing, and
Jayemdae Tome however are pretty suboptimal. Some good suggestions for swaps would be
Arcanis the Omnipotent,
Mulldrifter,
Jace Beleren, or
Sphinx of Magosi. Also the two cards mentioned in the Hug section, and maybe
Stroke of Genius too for good measure. It's blue, you can never draw too many cards.
COPY/STEAL
I like this suite also. How is
Sphinx Ambassador working out for you? At first glance it seems weak, but since you know your opponents' decks it might be working really well for you. Not sure on that one, up to you. I would say that
Spirit Away,
Soul Seizer, and
Domestication could go out and that
Blatant Thievery and
Phantasmal Image could go in.
HASTE
Strider Harness and
Ring of Valkas? You are trying too hard. Yeah, haste is rough in monoblue, but even high-performing red decks don't typically run more than 3 or 4 mass haste enablers. Solid replacements though would be
Lightning Greaves (of course, though a bit pricey) and
Sword of Vengeance (less pricey).
RAMP
Not much to see here, though if you're desperate you could add
Coldsteel Heart and
Paradise Plume. You seem okay here though.
OTHER STUFF
Dragon Mask I assume is mostly just bouncing your creatures. It could be
Erratic Portal instead.
Robe of Mirrors can take the cut. If you need protection for your general that badly, you could run
Whispersilk Cloak instead, but I think you should be okay.
Darksteel Sentinel,
Manor Gargoyle,
Sphinx of Jwar Isle, and
Creepy Doll are just not really great creatures in general, but are especially poor at the strategy that you are trying to push. What I think the deck needs are more creatures like
Inkwell Leviathan: big, scary, and destructive. For replacements, you could consider the Eldrazi.
Ulamog, the Infinite Gyre and
Kozilek, Butcher of Truth would be ideal, but they 'spensive tho.
It That Betrays and
Artisan of Kozilek are both decent stand-ins.
Darksteel Colossus,
Blightsteel Colossus, and
Colossus of Akros are big, stompy, and hard to get rid of. In-color, you could capitalize on the hand-returning aspect of the deck and run cards like
Denizen of the Deep,
Kederekt Leviathan, and
Tidespout Tyrant. Finally, you should probably invest in a
Jin-Gitaxias. He keeps your hand full and makes sure that your opponents can't drop a thing off of Braids for when you are ready to move in for the kill.
LAND
36 lands that all produce mana (some in multiples). Very nice!
Don't break it down yet! You can still make the deck awesome!