If there was an exclusion zone in place around Chernobyl, how was the plant still able to produce power? Reactor 3 was only shut down in 2000, a full 14 years later.
As I understand it, the plant kept producing power even though the cleanup of Reactor 4. It seems something that would render a 30km radius uninhabitable would also render the plant at the center of said zone uninhabitable too. Did people just commute into and out of the exclusion zone, only working their shifts? Was the plant remotely operated? Is the answer buried in some ex-Soviet archive somewhere?
This is less of a question of history and more of physics. Radiation has a wide variety of health effects, but determining what dose delivers what sort of harm is a complicated process. As an example, if you had a radiotherapy on, say 5% of your body mass, while the dosage for the target could be as high as 1 Grey (in some cases that's a fatal full body dosage) but since it only was 5% of your body, your actual dosage is probably closer to 0.05 Gy. When you start to consider that some parts of the body are more sensitive to radiation than others, and that some parts are more exposed, it quickly becomes very complicated to get an effective dosage estimate.
The reason Chernobyl made large areas around it uninhabitable isn't because people there would be getting high acute dosages of radiation. Most sources of heavy radiation were handled in the months after the accident by liquidators, and most heavy material wasn't ejected far. It's uninhabitable because living there for years and years would accumulate various radioisotopes in sensitive areas of the body (such as iodine in your thyroid), and would greatly increase the risk of various cancers and complications. The existence of a wide variety of tourist activities should be proof enough of the relative safety of Chernobyl, but safe for visitors (who bring in all their own food and water from outside), and safe for little children to grow up in are two different levels of safety.
So, as you guessed, workers simply commuted to the plant from outside the zone, or worked from facilities inside the zone temporarily. The Soviet Union, and later Ukraine were strapped for cash and energy, and there were three (later two) operational nuclear reactors available. Workers were given dosage limits and spending some time in Chernobyl certainly exposed them to radiation, but not enough to be considered harmful.
Decommissioning a nuclear plant at the best of times is an expensive process. Almost certainly it was cheaper to keep them on than to dispose of fuel and contaminated equipment. To this day Reactor 1 and 3 still haven't been properly decommissioned.
I found this article about one of the widows posted to one of the Chernobyl subreddits (4 hours after I made this post here, naturally). She worked at the plant and describes her day as follows:
Until 1988, I worked at Chernobyl on a rotational basis: a month at the station, and then a month off in Moscow. Our lab was located near the second reactor in a concrete room. I don’t know what kind of radiation was outside. Why should I know this? I worked like a zombie: I got up at five in the morning, went to the cafeteria, then boarded a bus that brought us to the “dirty zone,” we’d transfer to another bus, and ride that one to the station. I’d work a six-hour shift, and come home.