Bargain Play with major upside:
Carniceria Jimenez (you've got a few close - not all have taquerias for catering, tho.)
I'd try their Al Pastor first - to see if you like it ( I definitely do not.) I wouldn't hesitate to use them for carne asada, barbacoa, carnitas, rice, beans, several different salsas, guac, chips, tortillas. They tend to do their chicken in more of a fajita style with large chunks of chicken with peppers and onions, but if you tell them you'd like a finer chop, they would probably have no issue. I've mentioned Jimenez to a few friends for catering, and never heard anything besides fantastic for the price. Having the cervezas and margaritas flowing helps, but I wouldn't hesitate to use them at all for a bargain play. No idea of Big Star's prices, but I remember the first time I entertained the idea of Jimenez for catering, their prices were so low that I thought it might be a joke. Everything was perfectly fine - only quibble was the large chicken chunks and the fajita style prep of it. The carne asada, barbacoa and carnitas were perfectly fine, and quite good for the price. Again, the pastor - definitely not my thing at Jimenez, but maybe it'd be worth it to get your stuff from more than one place if you're dead set on Al Pastor. My stance on Al Pastor around town is that it's generally horrible (but I did love TC's!)
Also -
La Casa Del Pueblo on Blue Island. I've never used them for catering, but I'd assume they'd have no issue, and you'd be able to do tamales as well. If you've never been, and your crowd likes to think they are "hip," your side story can be, "This is where Rick Bayless shops." (He's filmed a few spots in his show wandering through their aisles.) It's a small grocery store on one side, and an awesome, awesome, awesome homestyle food cafeteria on the other side of the parking lot. The cafeteria also pumps out food orders from the kitchen - plenty of rustic cookin' madres and abuelitas manning the kitchen there. Love that place to death. Haven't been in a while, but anytime I'm within a mile, it's a no question stop.
We cannot be friends if you do not know the difference between Mayo and Miracle Whip.