I believe the issue is that the Matlab Compiler license is many thousands of dollars... Plus, Stuart probably needs the other toolbox like the Production Server.
Stuart, unless you're loaded with cash and want the compiler license, begin the process of painfully translating Matlab codes to ones you can use in the web. Otherwise, you'd need the standard matlab license $2200 + Compiler $X000? + Production Server $X000?, so close to $10K.
My relevant experience is: Matlab is great for protyping software, horrible for web-deployment unless you have serious $$$. That's why I learned Java. With Matlab, even after spending $$$ for Compiler, you'll have platform-dependent issues, as in you must compile Matlab in linux, windows, and mac versions (3 compiles) if you want many users to use your binary files directly. That means, you'll need a virtual machine to have MacOS, Linux, and Windows installed, with 3 installations of Matlab, with the same version of course so that the MCR library version works.
To put it on the web, you'll either have to have a docker container run the binary file, or, pay more for that Production Server license. The docker option has drawbacks, as in when the user access the binary file, there is a loading time to link the MCR to the binary everytime, like the delay in starting a new Matlab session.