Who in this current world wants to create or promote a growing community of free software developers, and chooses SourceForge as a platform instead of GitHub or GitLab?

Not that other alternatives are bad, but let me insist: especially if the intent is to attract more developers, GitHub has been THE choice already for several years.

Isn’t SourceForge synonymous with aggressive and intrusive advertisements all over the site and didn’t they get in trouble for inserting adware and spyware into projects’ binary downloads?

They did wrap installers in malware but have stopped now. Regardless, the site is very poorly designed and makes for a bad developer and user experience. To users and potential contributors, using SourceForge is synonymous with not caring.

I've registered a custom domain, which will be our primary user-facing point of contact. Developers use SF essentially purely as a Mercurial host; everything else is run over eMail.

Problem with those two is the first three letters. I'm fine with Bitbucket but decided against it in the near-term. Long-term, we'll probably move toward it.

Having strange and antiquated taste in collaboration tools is entirely consistent with wanting to revive Eudora. You may as well advise this person to "just use GMail."

Already do. I don't use Gmail's HTML interface (I always will prefer IMAP over an HTML gateway) but Gmail is my primary personal eMail server.

I absolutely hate git. I think its creator should be shot in the elbows, knees, and balls, and then broken on the wheel. GitHub has no Hg support, so it's out.

I thought long and hard about transitioning to Bitbucket. In the end, I decided against it in the near term, because I have two other projects going (Eudora revival for Windows, which is not the same program at all, despite the name, and then a LimeWire revival). I like to keep all my eggs in one basket, and if I tried to transition the other two projects to Bitbucket, I'd encounter inertia from at least one developer, sans doute.