When you tried the carbon steel pan, was it properly seasoned? They stick like hell before they are well seasoned, but seasoning them gives the carbon steel its non-stick properties. Woks are the ultimate tool for this, as they are carbon steel (so non-stick when seasoned) and their shape minimizes the amount of oil necessary to fry the rice. It is ubiquitous for fried rice across almost all of Asia.
Yeah but they use a lot of oil in those woks, and they get them really hot. Any Chinese street vendor with an open fire and cheap steel wok can do shit I can't dream of doing in my fancy ass American kitchen.
J Kenji Lopez-Alt has a lot of great wok content for American kitchens. In [0], he uses a butane torch to get the smoky wok flavor (wok hei) in a standard kitchen. He also reviews outdoor wok setups for those who want something close to Chinese street vendor-type vibe.
I cook with my carbon steel somewhat often, and it seems to have built up a nice thin black layer that keeps most things from sticking. Cleaning is a breeze, some dish soap and a couple scrubs. None of the black layer comes off.
Rice does not stick at first, but as it gets hot it does, unless I put around 3x the oil I would prefer. I have a gas range with a large burner so it gets very hot.