Same problem here, pretty much the same log file! Was working fine this morning, only difference is the network I'm on.
Tried:
Run as admin,
Compatibility settings,
Clearing Both Caches,
Uninstalling java, Runemate and RS, restarting and reinstalling,
Different Bots,
And combinations of the above.
I was getting this error last night as well, but it worked flawlessly on the other network, If its not sorted Ill update on if it works on the other network tomorrow.
Also going to try a virtual machine as was suggested in another post for a similar problem but would rather run it off my main os / live boot (If linux is supported)
Update 1:
Tested on a mobile hotspot and works flawlessly.
I was using a VPN which may have been the problem.
Also I noticed when using the hotspot over usb tethering I kept getting session expired errors, through a VPN and not.
Update 2:
Works on other network without VPN. Common theme here is the VPN.
Hotspot over USB may have been an issue due to not restarting runemate after changing networks.
