I'm not sure if the TC is properly bridged....
Yes, your setup is exactly right.
Also, this bit of advice threw me a bit...
my recommendation is once bridged swap the ethernet that goes to the C6300 LAN (ie NOT RED PORT.. must be Yellow one).. across to the TC LAN port.. <->
This is nor difficult... at the moment you have Ethernet from a LAN port of the C6300 to WAN port of the TC.. just swap that now to a LAN port instead.. it is not that different. In bridge the WAN becomes a LAN port in the TC.. but we find it somewhat unreliable.
This is despite the fact that I thought I bridged the TC.
The bridged TC can still act as WAP.. and in fact you have setup wireless correctly.. to act as such.
I have also been able to start my wireless backups from both of our MacBooks to the TC via it's network, although it did dump the backup process when I switched back to a C6300 wifi network to check something.
Ok.. this is where things start getting tricky.
Apple only support backups to the TC when your computer is directly connected to the TC.. When you swapped mid backup to the C6300 the connection is lost. If you started with the connection on the C6300 it might be OK.. if you wait long enough it might pickup again.. but swapping wireless in the midst of backup will definitely cause issues..
Why did you need to switch back to C6300.. ?? You can access the C6300 via the TC perfectly well.
One extra thing to do that might be worthwhile. Give your TC a static IP.. that helps you find it and stops it jumping around all over the place.
The best place to do it is DHCP reservations on the C6300.. but I will need to look up the method..
You can also setup the TC with static IP on WAN interface.. use the exact same numbers it has now with DHCP .. that will work but it is best to put those numbers into the C6300 as well.