The change of E depends on the change of m. c doesn't change.
If I have 500g matter and 500g antimatter and I put these together, then I will get an amount of energy that equals E = 1*c^2.
E and m change, not c.
What makes you think that c has to change, I really don't understand.
If you would want to calculate all the energy in the universe, then you need to stop the universe and measure the mass. Put this amount of mass in the formula and you will know what the total amount of energy in the universe is.
What makes you think that this total amount of energy would change? Or what makes you think that the total amount of mass at rest in the universe would change?