Hi Ethan
Apologies in advance for pointing you to my stuff but could you have a wee look at
www.alfi2fe.co.uk/EdSciTimemap.html. I have several datasets there. Most of them are loaded at start up but the activities dataset is loaded only when the check box is clicked.
Maybe I'm wrong but I reckon you could similarly arrange your datasets so that the JSON datasets are loaded on page load and that the KML datasets are loaded on demand.
If that is not close to what you want let me know and hopefully we can figure out between ourselves a way to get your desired results.
I work with OpenLayers quite a lot and from what I have seen, at best, you get a marker layer, a polyline layer and a polygon layer. A single timemap dataset may well span all of these.
Hope that helps.
Alan