Where to download beta of Sigil 6?
 

Does there happen to be a binary (Windows preferred) of the Sigil 6 beta?

No. The beta is closed. The creator(s) are working to solve the bugs. Perhaps there will be a new beta later.

IIRC they took it down after a sort comment period, leaving the crew to work out (and on) their plan.

I have a copy (windows MSI), but I would need permission to further propagate an un-supported (quirky :p ) version

Quirky it was.

If you enjoy-crave the newest and edgiest of software, you will eventually have to learn to build from source. That is the joy/aggravation of the gift of GPL3 code. Myself, I will wait

There is also no guarantee that this next released version will be entirely alike the beta was and you might have to learn how to do things all over again in a different way.

I totally agree with paxmark. You could try downloading the clone "0.5.9" but you should keep in mind that it is work in progress and not advicable if your starting out. I repeat, try 0.5.9 clone at your own risk.
Talking about clone, does anyone know how to download entire source folder of Sigil clone with GitHub client?

I know nothing about the GitHub client, but from the git command line you just run the command that is displayed on the Sigil source website, of:
Change the URL of course if you have made a remote clone of the Sigil respository and want to point to that instead.

If you are on Windows I use TortoiseGIT, mostly because I also use TortoiseSVN so I'm used to that style of explorer integration. It can do more than everything you need, though it can get horribly confusing to begin with the myriad of options. I think John summarised it well in an email when he said git is not so much a learning curve but rather more like leaping off a cliff.