After ruminating on it through the night I came up with a solution. If someone knows of a better way to do this, by all means share it.
What I did was create a variable that was global to both the "Tprime_converger" function and the "Tprime" function, which is the function where the system of ODEs is defined.
At the end of "Tprime", I added the computation :
Taco = T - dT;
and I changed "Tprime_converger" to :
function [value,isterminal,direction] = Tprime_converger(t,T)
value = abs( sum(Taco(:)) - sum(T(:)) ) - 2*eps;
isterminal = 1;
direction = -1;
end
I checked the values against computations using the same functions without implementing any 'Events' where the ODE solver is part of a loop with its own convergence checker built in at each time step the loop iterates on, and the solutions differed with a relative difference on the order of 10^-14; essentially no difference. The upshot is that the implementation using 'Events' converges significantly more rapidly.
-ryan