I do not know what is the motivation for you to use the live scripts. I really find this a cool way of documenting and something which approaches a bit what you can do in Jupyter Notebooks.
In fact, I have been using successfully Jupyter Notebooks with the matlab engine in the last two years to run matlab code. I have worked that way since I have some python background and did not know live scripts until recently. Just lately I have got in touch with matlabs live scripts through a colleague and we have noticed latency which I do not experience through Jupyter Notebooks. I guess the mechanics here are really different and the Notebook approach almost resembles running bare scripts with a bit of overhead on the matlab engine.
Maybe you can give Jupyter Notebook a try and get better performance and with slightly better documentation capabilities with markdown.