• Blood's alpha source code was leaked at one point and can be found fairly easy. People haven't done much with that.
• Atari worked with the community and gave Transfusion a quitclaim agreement, which allows use of the game resources for that project; but that's lost any kind of momentum.
• Cradle to Grave (the PostMortem project) kinda went the same way.
the XL Engine seems to be on hold, but luciusDXL still makes blog posts, so the jury is still out on that one I guess.
• BloodCM seems to be doing a really good job of converting the materials over to the eDuke32 engine. Kudos to that/those guy/s.

Others that have fallen by the way side: zBlood, Blood Source, B.L.O.O.D., Blood2Resurrection

Sadly it looks like community efforts are so spread out and in some cases out and out at war with each other, that seeing a full HR remake of Blood is just a pipe dream unless the deep pockets step in.

I couldn't agree more with you. I'd love a Blood Redux too. Blood is by far my favourite shooter. But well, the XL project is our best hope. The creator is focusing on Daggerfall right now, but I think Blood comes next.
Until XLBlood is released, try the game DustyStyx suggested, BloodCM. Even if it is not perfect, it's pretty well done and achieves a true "Blood experience".

For whatever reason I only just found this. Well, I have firsthand experience working in the game industry, so there's that. There's also having looked at nearly every commercial game with released source in existence, and keeping up with the nuances and possible legal considerations involved in each case. There's also the recent Keen source debacle which you can feel free to look into for an example of how these things go the way they do.

You're right in a minor sense that someone would need to look at the code, but it's not for the reasons you think. It'd be to add legal disclaimers at the top of every source file. A guy named Sponge who works on QuakeLive was tasked with doing this for the Keen source release (to his credit, he did also clean it up and removed the Keen 6 portions as that's its own legal quagmire). It was never released and I was told by him that it most likely won't be. It should be obvious to you, but the reasons aren't the source having been processed or not. I'll leave it as an exercise to you to apply the abstract reasoning here in this case.