Great work Szabolcs! From your documentation I learnt about the option
BaseStyle -> {FontFamily -> "Latin Modern Roman"}
that you can give to plots. I had no idea that you could do that. It works beautifully without the MaTeX package, at least in the simple cases that I tried, and it is as fast as the default. It will be noticeably non-TeX-like for greek letters, and maybe in other cases.
Your example typesets almost the same this way:
Plot[Evaluate@{Sin[x], Normal[Sin[x] + O[x]^6]}, {x, -Pi, Pi},
Frame -> True, BaseStyle -> {FontFamily -> "Latin Modern Roman"},
FrameLabel -> {"\!\(\*FormBox[\(x\),
TraditionalForm]\)", "sine of \!\(\*FormBox[\(x\),
TraditionalForm]\)"},
PlotLegends -> {Style[Sin[x], FontFamily -> "Latin Modern Roman"],
Style[Normal[Sin[x] + O[x]^6],
FontFamily -> "Latin Modern Roman"]}]
Unfortunately, BaseStyle does not extend its influence into PlotLegends. I would regard this as a bug.