It admittedly doesn’t compile to HTML and the compile-time can be on the order of minutes for very large documents, but are these really deal-breakers?
If you really don’t like LaTeX, have a look at org-mode, which seems to be able to fulfil most, if not all, of your requirements (not sure about compile times).
I was doing an algorithms course with lots of mathematical formulas last year. Org was a godsend for completing the homework assignments.
I think it's lacking the #include/#input feature, and I'm not sure whether it supports labels and internal references, but apparently it has some form of bibliography.
Pandoc does provide a way to link to section headings, but it doesn't yet have a generic system for autogenerating numbers and producing references to these, like LaTeX's \label{} and \ref{}. It does, however, have a system for creating running example lists: http://johnmacfarlane.net/pandoc/README.html#numbered-exampl.... This can be used for numbering equations and referring back to them, but it is considerably less flexible than LaTeX.
Pandoc has extensive support for automatic citations using CSL stylesheets: http://johnmacfarlane.net/pandoc/README.html#citations. BibTeX and BibLaTeX files can be used as the database, or YAML citations can be included in the markdown document itself.
LaTeX formulas can be embedded in markdown. They can even use macros defined in the document. Formulas can be converted to MathML or native Word equation objects, depending on the output format.
Pandoc can also be extended using "filters" that operate directly on the parsed AST. Here's an example of a filter that finds tikz diagrams and converts them to embedded images that can be displayed on the web: https://github.com/jgm/pandocfilters/blob/master/examples/ti....
At a minimum, it does markdown with embedded LaTeX and outputs pdf.
I'm not sure why you want the ability to embed LaTeX formulas. LaTeX formats math gloriously, but its syntax is not any less horrid for math than it is for anything else. I'd rather write "sum(i <- 1..10, frac(t_i, sigma^2))" than "\sum_{i=1}^{10} \frac{t_i}{\sigma^2}" but maybe that's just me.
Obviously the big step is for it to be able to output LaTeX so that the equation capabilities and such will be directly exposed, but Asciidoc is pretty awesome already in my experience.
I can see how you might not like the language itself, I don't either. But inconsistency is rather orthogonal quality. I think it is actually pretty consistent, which is respectable in its own right.
Send an email to the address in my profile and I'll fast-track it.
LaTeX is a horrible language, inconsistent and badly designed and unpleasant to look at. TeX is good at what it does but the whole system is horribly slow to compile documents. Documents will compile fine with some frontends but not with others. Markdown is not feature complete enough.
The scientific community is unfortunately stuck with LaTeX for the foreseeable future. Seems like every day someone asks me how to do something that should be very simple, which inevitably involves loading some obscure package.