Collaborative paper-writing with non-LaTeX-using colleagues
Excluding LaTeX-focused online collaboration services, such as ShareLaTeX, due to your new collaborators' preferences, I think that you have pretty much two major options, as follows:


Overleaf (formerly WriteLaTeX)
Authorea


Both online academic collaboration services support simultaneous use of LaTeX and WYSIWYG rich text mode, Authorea also supports some other formats, such as Markdown and HTML. Both services (to various extent) offer other nice collaborative features, such as data sharing, version control, revision notes and much more. Due to multi-format support, I would prefer Authorea to Overleaf, however, the final decision should be made upon a comprehensive comparison of both services across all available features and your detailed requirements as well as some testing.

P.S. Just for completeness, I will mention two other options. The first is to use blog engines that support both WYSIWYG and LaTeX (most of the major ones do: from WordPress to Jekyll). It's a decent option, but I would prefer one of the above-mentioned dedicated services, for multiple reasons. The second option is to self-host RStudio Server (or maybe a custom Shiny application), which would allow academic collaborative writing, using RMarkdown, but IMHO this is the worst solution possible, as trying to implement various needed features and solve issues, such as version control integration, would bring you and your collaborators a lot of headaches.