An App to open a group of related documents?

You'd think everyone needed that, right? You've run up against the limitations of the Finder. So maybe an alternative is in order.

Check out Conjure; it does pretty much what you ask. It's a very different way of organizing. http://www.conjurebunny.com/Conjure/Organize.html

Or Raskin; it also allows some grouping (on sale BTW as part of the "productivity bundle").

You could also just move all the documents into a folder and just select-All and then re-open them. You'd have to save the Safari pages as weblocs, but possible. I'd take it a bit further and use a Mavericks tag like "Project1" to do this. I use Leap, and it makes it possible to show email, web pages, and documents all at once with the same tag or tags. Very nice. Default Folder X, in conjunction with tags and favorites might be helpful as well.

Another solution for project work I've used is DevonThink. You can reference files in DT's database, so you could have a "Project1" folder with all the files you need, even though they might be actually stored elsewhere. You can just drop webpages on, and either store them as URLs, which you can view right in DT (!), or as complete web archives, in case you fear the content will be gone by the time you get back to it. Where it's better than tagging or alternate Finder applications (although you can tag with it) is that you can also create notes right in it, like "remember to fact check the citation" or whatever. And you can export stuff, archive it, all sorts of goodies. And since you can open much of the stuff right in DT you could avoid the problem of having to open Safari and Text Edit and maybe some other stuff. I think it's your best bet; it's a very popular system for research work like what you seem to be doing.

I'm kind of wondering why Spaces doesn't work for you. When you're not actually doing something in these windows it shouldn't be slowing your system down that much. But even if that was sorted, check this other stuff out.