How can I export the frequency response from LTSPICE without phase wrapping?
I think you cannot fix this in LTSpice.
I didn't find hard evidence, but very plausible evidence.
If you hover over the angle axis (you'll see a ruler) and left click it, there is an option to Unravel Branch Wrap. Why would the option here if there were no reason to unravel it?



If you deselect it, you'll see the same output as MATLAB shows.  

So, I think you should unravel the data yourself, in MATLAB.