Yes, we do have online versions up and going and have been using them in-house. All are built using jsPsych to really handle stimulus delivery, but I've been working with both Cordova and JATOS for other aspects of management. Cordova is nice in that you can easily get onto things like iPads as well, but JATOS gives a very nice platform to let experimenters manage studies, their data, etc. The way I have it setup, though, is that for each experiment I want to run, I have all the MST code and resources (e.g., images) and I have a "setup.html" file that does all of the things like assigning people to conditions. That setup code changes across experiments while the main MST code remains the same.
Shifting to online, though, means you'll need something to host the code. I've had good luck even running a simple virtual machine (e.g., VirtualBox) that runs a small Linux web server.
In the end, here -- I've got several variants of the MST up and going and we're using them just fine. Being remote does mean a bit more setup on your end, so it's not quite as simple as just handing out the standalone. I can put a simple JATOS study-test MST up on the GitHub page if people like, though.
Craig