How can I seamlessly make my phone a network drive?
There are several apps in the Play Store that can do this. One I've had some luck with is Samba Server.  To see other options, search the store with keywords like file server. Some functionality will require a rooted device, so YMMV.

Each of these have their pros and cons. I recommend trying a few to see which fit your specific situation best. Hopefully one of the free ones will work best for you!