Given that the main point of using LaTeX in Markdown is familiarity of users, using $ and $$ is actually the ONLY proper choice. But yeah, it leads to problems, which is why I would not use Markdown in the first place, but some Markdown inspired format which mixes better with $ and $$.
This is why I prefer AsciiDoc. It's consistent because there's only one implementation, it's less ambiguous, and more predictable. Although it takes a bit longer to remember all the syntax, it's not difficult, especially if you're only going to use the same subset of features that markdown supports since it supports most of the markdown syntax as well. I also much prefer the flexibility with tables compared to markdown. I just wish there were more parsers/converters other than the main ruby one and the transpiled JS one, although I know there's work being done on other language implementations.
As an example for math/equations, inline math is stem:[sqrt(4)], which defaults to AciiMath, but can be changed with a page attribute. To specify inline, LaTeX is latexmath:[\sqrt(2)] and AciiMath is asciimath:[sqrt(2)].
For blocks (which you can replace stem with either latexmath or asciimath to specify),
True, it's more verbose, but I'd take increased verbosity and standardization over increased ambiguity and inconsistency since every markdown parser and renderer translates things a little differently, which is why there's things like Babelmark[0]. That verbosity also provides consistent, more powerful features like multi-line table cells, table cell spanning, table nesting, sidebars, admonitions, footnotes, table of contents, image embedding, cross-doc references, latex-like includes, etc. that all follow a similar inline and block syntax and are rather clear from a glance.
It's certainly not perfect, but I much prefer it for the flexibility and consistency to the dozens of markdown implementations that all do things a little different and not needing to drop down into HTML when I need to do something just outside of markdown's capabilities.