I'm writing my master's thesis in Minion Pro using LyX and I would like to use that font for math, too. For PDF output I use LuaTeX due to several nice features I got used to in the past (such as easy font configuration).
To get Minion Pro to work in math I use the following code in my preamble (copied from https://tex.stackexchange.com/a/38093):
\usepackage{amsmath} % always load before mathspec or unicode-math
\usepackage[math-style=ISO]{unicode-math} % try sans-style=upright
\defaultfontfeatures{Scale=MatchLowercase,Mapping=tex-text}
\setmainfont[Numbers={OldStyle,Proportional},SmallCapsFeatures={LetterSpace=6},%
BoldFont={Myriad Pro Bold},BoldFeatures={LetterSpace=3}]{Minion Pro}
\setsansfont[Numbers={OldStyle,Proportional},LetterSpace=3]{Myriad Pro}
\setmonofont{Crystal}
\setmathfont{xits-math.otf}
\setmathfont[range=\mathup/{num,latin,Latin,greek,Greek}]{Minion Pro}
\setmathfont[range=\mathsf/{num,latin,Latin,greek,Greek}]{Myriad Pro}
\setmathfont[range=\mathbfsf/{num,latin,Latin,greek,Greek}]{Myriad Pro Bold}
\setmathfont[range=\mathit/{num,latin,Latin,greek,Greek}]%
{Minion Pro Italic}
\setmathfont[range=\mathsfit/{num,latin,Latin,greek,Greek}]%
{Myriad Pro Italic}
\setmathfont[range=\mathbfsfit/{num,latin,Latin,greek,Greek}]%
{Myriad Pro Bold Italic}
\setmathfont[range=\mathtt->\mathup]{Crystal}
\let\mathbf\mathbfsf
\let\mathbfit\mathbfsfit
\AtBeginDocument{\let\phi\varphi}
It works nearly as expected but the symbols like sqrt etc that xits-math provides look really strange:

Is there a way to fix this or (maybe even better?) another solution to achieve good looking formulas with Minion Pro using LuaTeX?
(I know there is MnSymbol but I couldn't get it to work correctly with LuaTeX neither. I also don't want to use Minion Math because I prefer solutions that are free (at least free as in free beer)).
Thanks in advance!