On Discord I got a tip from Tyson to simply simulate what I need in place, export the animation as cache files and then link the cache to my mesh. It was a great and simple idea.
In case you have encountered a similar situation here's a more detailed guide:
Use the Export Particles node to export what you need in a tyCache format with the coordinates set to "world". Now deactivate all the events in the flow. Then load in the saved cache files through a tyCache object and set the coordinates inside the tyCache options to "local". Because it's now set to local you can link the tyCache object to your moving mesh and it will follow along nicely. If you are using tySplines and tyMesher like me and need the bindings exported as well, it doesn't work. However in the Particle Export node you can include Splines to be directly exported as geomentry with your cache files... this will export what your current tySplines object is generating as geometry so beware of the resulting file size per frame. All you need to do now is add your tyCache object to the list of your tyMesher and activate the option to consider particle meshes.
In case you have encountered a similar situation here's a more detailed guide:
Use the Export Particles node to export what you need in a tyCache format with the coordinates set to "world". Now deactivate all the events in the flow. Then load in the saved cache files through a tyCache object and set the coordinates inside the tyCache options to "local". Because it's now set to local you can link the tyCache object to your moving mesh and it will follow along nicely. If you are using tySplines and tyMesher like me and need the bindings exported as well, it doesn't work. However in the Particle Export node you can include Splines to be directly exported as geomentry with your cache files... this will export what your current tySplines object is generating as geometry so beware of the resulting file size per frame. All you need to do now is add your tyCache object to the list of your tyMesher and activate the option to consider particle meshes.