Challenging, yes, but not impossible.
When manually updating your FastDL cache, your copying the cache from your server (not your client) to your file host DL location, right?
(This would normally be a 2 step process. Copy server/cache folder to your local machine (Desktop/etc), then upload to the host DL server.)
I notice you have another admin (at least, according to your debug file). Does that person have problems?
As for the data/ULib folder not being on your local machine, that is most likely due to you never having run a local/listen server.
If you have run a listen server with ULib installed, most likely, the same error is preventing data files from being created.
The only other option I'd suggest, and yes, it would take a long time, is the following.
First, because I believe it's a local issue, let's not bother your server users (other than seeing you reconnect many times)
All locally -
Shut down Gmod.
Shut down Steam.
Delete all files in your <local path gmod>\cache folder.
Move most your <local path gmod>\addon\<folders here> to a backup folder. Leave only the ones made by garry for valve games.
(those are counter-strike, day-of-defeat, hl2_ep2, left4dead, left4dead2, portal, tf2. and zps)
Start steam, start Gmod, connect to your server. It will take a bit longer of course to connect, because it has to rebuild your local cache.
See if you get the error.
If that does work, start the cycle of shutting down Gmod, copy back one or two at a time (NO MORE) of the addons you moved back to <your local gmod path>\addons folder, restart Gmod, connect to your server.
When you've added back the (I'm suspecting) addon that causes the issue, you'll start getting the error again.
Go back, remove it.
Report to us what it was.
If that doesn't work;
Now is the time you'll have to bother people that want to connect to your server.
Password protect it to keep people from joining during your testing.
Do the same as above. Remove all addons except valve ones, reupdate your fastdl cache every server restart/addon change.
After removing all the addons and updating fastdl cache, connect.
If error, we've at least determined its gamemode/fadmin/ulib issue.