It is an important question, I need to find that out too. Does a GVW upgrade increase your GCM? I suspect not but I might get a surprise.
2000kg ATM includes the towball weight, so that trailer would be about 1820kg-ish GTM and the 180kg comes out of your vehicle's GVW.
Toyota's stated 2500kg is ATM though just to confuse the issue!
Out of interest my 2011 SR5 petrol auto has a GCM of 5060kg, towing 2250kg and the difference is the GVW of 2810kg (the diesel auto is 30kg less in both GVW and GCM).
Your 2013 has the same GVW as the 2011 diesel auto at 2780kg and towing at 2500kg, so Toyota did increase the GCM by the same 250kg, GCM=5280kg (petrol auto 2013 is 30kg higher in both).
So at least for me if can get an Engineer to see logic that I can upgrade to 2500kg towing, that the GCM can go up too as the cars are identical other than appearance. Not sure if the same logic applies to a straight GW upgrade though like you want.