Finally, I'm pretty confident that when you double click a WTV file (associated with MC) in Windows Explorer, it does stream it (not sure who, if anyone, transcodes it) and that works perfectly.
No, that's not right, and that's the problem. When you play a file from a network location (whether it is a mounted network drive with a drive letter, or just a UNC path you browse to) it plays the file the same way it does a local file (it is NOT streamed). The only difference is that the "disk" is slower because it is over the network (but, yes, a gigabit LAN is fast enough to play most things without issue, unless you get up above 100mbps files).
When you play a file on MC in "client mode" where MC does NOT have local access to the file, the
server has to first convert the file to a format that it is able to send out over the Media Network port. Windows Networking and network shares are not used at all, and you can actually have them completely turned off.
This works well with many TS files because they are either already in a "streamable" format, or they are easily converted. The same is not true with other file types. Like I said, this system is really designed to allow you to play files from across the Internet where you can't have direct access to the source files (unless you have a VPN set up, and even then, that would be VERY slow). So, for example, I have my MC Port forwarded through my firewall at home. I can take my laptop across the country, and still open MC up and connect to my server at home from anywhere in the world I have Internet access. Even though I cannot browse and connect to my home PC's network shares through Windows, I can still play all of my files in MC. With music and some video types, this works beautifully. With other videos, this doesn't work very well: the files take a LONG time to start playing, and even once they do, you can't fast forward because only a small portion of the video has been loaded so far (it plays as the file is still "downloading"). I called it "streaming" above for simplicity's sake, but I think what it is actually doing is more of a progressive download, like YouTube.
Anyway, what you want to do to solve the problem is import your files into the
server copy of MC using their UNC path, rather than their local path. Then, when you play them using the client machine, that copy of MC will be able to "find" the files on the network the same way it works when you manually browse and play the file.
So, to give you a real world example... Say your file server and MC server is called servermachine.mynetwork.lan (192.168.0.10). The media files all live at C:\Users\Public\Media\ and you have the "Media" folder shared on the network as a share called "media".
In MC's auto-import, you would NOT want to monitor C:\Users\Public\Media\. Instead, you want to monitor \\servermachine.mynetwork.lan\media\. All of the files you have in the library already that have their [Filename] tag listed as C:\Users\Public\Media\blah\blah\blah.wtv need to be changed to \\servermachine.mynetwork.lan\media\blah\blah\blah.wtv. If your network isn't configured such that you have working hostnames like servermachine.mynetwork.lan then your best bet is to just use the IP address directly (the server will need to have a static IP address) like this: \\192.168.0.10\media\blah\blah\blah.wtv
This is easy to do using the Find and Replace tool in MC, but you may need some guidance to prevent problems. Basically, what you want to do is move the entire current contents of your media folder off to a "safe place" that MC doesn't know about (which will break ALL of the files in MC), then use the Rename, Move, and Copy files tool to do a Find and Replace and replace C:\Users\Public\Media\ with \\servermachine.mynetwork.lan\media\. Once that is done, you can close MC and move all of the files back to where they started and then MC will "see" them again. It is safest to move them first because if you just do the Rename, Move, and Copy files tool thing first, it will try to actually move all of the files from the source to the destination (which are effectively, the same) and it'll probably get all screwed up (overwriting the files that you are moving currently and whatnot).
When you have it set up that way, you don't need to have network drives mounted on any of the machines, because MC can use the UNC path (those that start with \\) just as well as it can use paths that start with a drive letter. When you play files on the server, it will actually access them through the "network" (pointing to localhost) but this works fine.
Note: The MC server and the file server DO NOT have to be the same machine on the network, and the files don't have to be on the C drive, I'm just using those as examples.
If you describe in detail exactly where your files live on the server, and how your addresses on the network work, I can explain exactly what to do for your situation.