Let's make sure we understand the actual operational parameters you need.
Does the Storage Device need to have onboard memory and copy a data set to your removable drive while continuing to store data to onboard memory ?
Or is it OK for you to stop the Storage Device, remove the storage media, move it to a computer and copy the data off it, replace the storage media, and restart data logging ?
Is a network connection (FTP, HTTP, or something else) a suitable alternative for copying the data from the Storage Device to a PC ?
The Red Lion G3's (not the Kadets) and ProducTVity Station have USB Host ports, but the DataStation Plus doesn't. I know they can copy log files to the removable media on a schedule but I haven't done an application where those files were copied on-demand.
There are certainly serial data loggers that might do the job. One that I like the look and price of is the Brigantine Electronics "Dogcatcher" serial data logger.
http://www.brig-elec.com/index.html