ejolaus wrote:
Is this possible at all?
"At all" is pretty open-ended. As celliot147 suggested, you can do this with a developer account. You don't actually need access to the original source files. There is a way to brute-force replace a signature with your own and then notarize it. Just make sure that it really is a legitimate app. There will be a record associating your Apple Developer account with this binary. If the binary is one day found to be malicious, Apple could potentially take action against any Developer account that had previously notarized it.
Also, if these are open-source apps, then you may be able to build them yourself. Since you aren't downloading them in this case, Gatekeeper doesn't get involved. You would not need a paid Apple developer account to do this.
And now that I think about it, I guess you could manually strip the Gatekeeper attribute from the downloaded file using the Terminal. Just make sure that you are 100% certain the download is legitimate and not malicious. This option is a bit shady so you'll have to Google it yourself. It's a legitimate debugging technique using built-in Apple tools. But this is an end-user support forum and sometimes those low-level hacks are considered too dangerous and get a post removed.
And going in the other direction, it's also possible that these apps haven't been correctly constructed in the first place. That may be what is actually blocking you from installing them. You probably won't be able to fix that.