Manaless ichorid seems ideal - no boarding and free mulls. If you don't have bazaars just use breakthrough and cephalid colleseum like legacy builds. Don't bother with serum powder since you have free mulls - use leylines instead to keep your bridges alive and for the mirror, and don't forget to use angel of despair main since you can't side
This seems like sound advice and is probably your best bet, OP.
If you decided to stick with UW, I would definitely cut Arcane Denial for almost any other two mana counter—it's that awful. Bribery is fun but ridiculously slow, especially without acceleration in the form or drains or moxen or whatnot. If you expect any power at all, definitely consider maindeck Null Rods. Or at least swap Black Vise for Pithing Needles. Also, I'd drop the Mazes since they are useless a lot of the time. In general, that deck list you posted is pretty horrible in my opinion. Not trying to be mean or anything but meh..you could do better with a pretty similar card pool.
One thing I have always thought about is using Canonists in an aggro-controllish build of Forbiddian to take the place of Arcane Lab. I dunno how viable it would be, I've never tested it, but it's a thought. You could even cut Wastelands to run Back to Basics with lots of sac lands and basics. I guess I might as well be brave and venture a deck list
I was thinking something to the effect of
Creatures4 Canonist
4 Ophidian
1 Darksteel
Countermagic4 Counterspell
4 Force of Will
2 Forbid
3 Misdirection
Artifact2 Powder Keg (good against random aggro decks)
4 Pithing Needle
2 Sensei's Divining Top
Other3 Back to Basics
1 Tinker
1 Balance
1 Brainstorm
1 Echoing Truth/Hurkyl's Recall
4 Flooded Strand
2 Polluted Delta
2 Tundra
2 Plains
13 Island
Is this deck any good at all? I don't know. Looks like it could be interesting though. Meddling Mage could be used over some of the more defensive cards too.
Since budget is a consideration, other cheap common cards I am thinking of include Force Spike, Daze, Seal of Cleansing, Mystic Remora, Repeal, and maybe even Swords to Plowshares.
Mainly I don't know if UW is that good a choice though.