A few clarifications:
The Key to Time arc was designed by Graham Williams, the producer of the show.
The individual stories were written by various writers, including Douglas Adams - I don't think his story is great, though it has good moments.
The Ribos Operation by Robert Holmes
The Pirate Planet by Douglas Adams
The Stones of Blood by David Fisher
The Androids of Tara by David Fisher
The Power of Kroll by Robert Holmes
The Armageddon Factor by Bob Baker and Dave Martin
The script editor was Anthony Read for the season.
Douglas Adams would be the script editor for the following season, and contributed to script editing on The Armageddon Factor, including rewriting the final confrontation with the Black Guardian.
What's interesting about that season, and is something that has been mentioned here before, is that most of those stories could very easily be turned in D&D scenarios. Three of the stories feature planets that are at a medieval tech level or lower - two have minimal amounts of technology which could easily be substituted for magic, but the third would be a bit more difficult and require some work. One story is (mostly) set on modern-day Earth, but in a rural area where modern technology isn't that important, and the story leans heavily into folk horror tropes that would work well in D&D anyway. The remaining two are pretty unabashedly sci-fi, but one could, with some work, be transformed into a wacky Spelljammer adventure. The remaining one, however, would be pretty tough to convert.
Basically:
TRO: Easy to convert. Ribos is a planet that is currently at a medieval level of development. It would just need to change the offworld visitors to Ribos as being from some other country or continent and switch out their technology for magic. Besides that, it's flush with D&D-type stuff: there are crown jewels locked away in a citadel guarded by monsters, two rogues trying to pull a fast one on the out-of-town nobility, prophesies of doom, myths of the gods fighting in the heavens, and a good old-fashioned dungeon crawl in catacombs...
TPP: Hard to convert. It could be turned into a Spelljammer campaign on a more massive scale than most, with a helm of a crashed ship now moving planets. The psionic subplot might be hard to convert to 5e.
TSoB: Somewhat easy to convert. The parts on Earth are just your typical evil druid plot, using evil earth elementals; even if it's in the present day, adjusting it to a more D&D-esque period wouldn't require much work at all. The parts on the villan's spaceship would be the tougher section, although since the spaceship is in hyperspace immediately adjacent to the stone circle, it could just be re-skinned as a citadel in the Feywild with the stone circle being a fey crossing (and the villan is very evil fey-like).
TAoT. Easiest to convert. Tara is a planet where, after a plague killed off most people and the titular androids were built
en masse to take over most of the work, the remnant population re-created the world as a sort of Renaissance-era feudal playground. There are swordfights, kidnapings, monsters, castles, political intrigue over the succession - lots of your standard D&D tropes. Basically, Tara is a world where only the role-players survived and re-created it as they wished lol. The remaining technology could easily be re-skinned as magic (
"Taran rapier: This rapier does an additional 1d6 lightning damage on a hit"). The only real issue would be the titular androids; since them breaking down and malfunctioning (always at the worst times of course) drives much of the plot, they would have to be more magi-tech than being the result of cloning or the like; maybe something like human-looking totally-mechanical warforged (without the whole soul situation).
TPoK: Somewhat hard to convert. As it's a colonist vs colonized plot, the natives and the monster would be easily to convert to D&D terms, but the colonists and their huge refiinery would be quite a bit more difficult. Poweful mages having created a huge citadel that drains energy from the area, perhaps?
TAF: This would be the hardest to convert, as it's by far the most sci-fi, as well as the most modern with its themes of the horrors of war and mutually assured destruction. With a lot of work, it might be able to be coverted to some huge magic war that got so seriously out of hand that the Twin Cataclysms or the Day of Mourning are tiny squabbles in comparison, but it would be very weird D&D indeed.
So, it could work as a Rod of Seven Parts quest. Although the Key only has six parts, the tracer which tracks down the parts of the Key is actually what holds the Key together, and is given at the start, so it's the
de facto first of seven pieces.