Hey!
I don't have a conversion tool, but if your project uses prefabs for objects with text, swapping out the objects shouldn't be too bad! I was thinking what you're thinking - I really made STM with dialogue boxes in mind, which there's usually not many of in a game. So swapping out those few objects shouldn't be too painful.
If I2 can print text to both Unity UI and Text Mesh Pro (that it says on the asset store), I don't see any reason why it can't print to STM... I do remember that for my Adventure Creator compatibility, AC only explicitly supported certain rendering classes, so in that situation, I had it send text to a disabled Unity text renderer, and then have STM copy that hidden text immediately after. So... that just means one extra line of code when you're getting text from a dialogue asset, in this worst-case scenario.