Hi Chris,
I have an idea: Your link could just be the usual tasklist link with an additional URL query parameter, e.g.: localhost:8080/camunda/app/tasklist/default/#/?startProcess=my_process. You can then write a plugin that, when it is initialized, reads the complete URL and depending on whether or not the startProcess key is present in the URL opens the start process modal.
The tricky part is then to actually perform the magic to open the modal. You could either try to programatically click on the start process button and on the name of the process instance, which would be tricky as there are asynchronous requests and pagination. Or you could replicate some of the logic of the start-process dialog, which can be found on Github: https://github.com/camunda/camunda-bpm-webapp/tree/master/ui/tasklist/client/scripts/process/plugins/action/modals
Would this work for your scenario?
Cheers
Sebastian