I would guess that the majority, if not nearly all of the hot dog joints in Chicago do not prepare their own beef. Why do you think they are slinging hot dogs and not running a French cuisine restaurant with custom made pastries? To me, a Subway menu is too complicated.
As CSD has said numerous times, what do people expect when they see a hot dog cart? HOTDOGS!! K.I.S.S. He's been very successful and sells one dog product and drinks.....not even chips. I think he's onto something. Beef sandwich also takes a lot more time to prepare than a dog. The au jus should be watery. We dip each end of the bread (ends trimmed off) in the au jus about a couple inches, then ladle on more after the beef is in the bun. The juice should drip at least down to your elbows as previously stated. We have a brick and mortar Vienna joint, but on a cart, I'd keep it simple and just push a great-tasting dog.
We have Chicago-Style in our name, but that doesn't mean diddley outside of Chicago. You have to go with local tradition, as if California has any tradition.

Find out where most of the people in your area are from and go with that. If they're all from New York, all you need is brown mustard and sauerkraut and a pan of hot water. Here in Charlotte, we sell more dogs with chili and slaw than anything else.
Distributors deliver, although most will have a minimum order. If this is a problem, make friends with your nearest restaurant that uses the same distributor and have them drop off your order there and then go pick it up. I do this all the time with my secondary distributor, as I usually don't meet the minimum with my non-Vienna distributor.
I myself don't see working a cart all day and then coming home and preparing and cooking beef, which also would be illegal unless you do it in an inspected kitchen. Shoot.....throw the dogs in the water, sling em on a bun, count your money, go home and pop a beer and watch South Park.