Here's a quick inventory of the current tagging status of multi-mission space programs:
- Mercury: "project-mercury"
- Gemini: "project-gemini"
- Apollo: "apollo-program" + individual tags for Apollo 10-17 and Apollo-Soyuz
- Space Shuttle: "space-shuttle" + the individual orbiters "shuttle-columbia", "shuttle-challenger"
- Vostok: "vostok-program"
- Voskhod: "voskhod-program"
- Shenzhou: "shenzhou"
- Salyut: "salyut"
- Explorer: Individual "explorer-1" and "explorer-3"
- Mars: Individual "mars-3"
- Surveyor: "surveyor-program" + individual "surveyor-3"
- Venera: "venera"
- Mariner: "mariner"
- Voyager: "voyager"
- Pioneer: "pioneer"
- Luna: "luna"
- Chang'e: "chang-e"
- Sputnik: "sputnik"
It looks like generally, only the programme name is used, with disambiguating tags only being added once the number of questions has become quite large, but that's just an observation.
The early days of Explorer satellites looks somewhat similar to Kosmos satellites, being a catch-all name for all orbital mission, so I agree with you on the satellites being very diverse.
If I were to form an opinion, I think your solution with "explorer-1" and "explorer-2" is just fine, the only issue I have with it is that other questions about explorer satellites can not be found by clicking on tags on the question in question, unless the "explorer-1" tag is added, which is technically incorrect.
What's more, pretty much any new question about any or all Explorer mission will increase the need for a programme tag.
A general "explorers-program" (or "explorer") tag would probably have solved the issue just as well, while at the same time being slightly more future-proof. In the very long run however, individual missions should be re-introduced.
Does that sound okay?
I still think it's okay.