In the same company mate. Engines are rated at TOGA for 10 mins. reference is in the RTOW charts I think. No start limits as EEC looks after it as you say. Normal start limit is 700c and 885c inflight. If you bring up eng limits on EICAS you will see normal limit written but not when on lower mfd.
I also answered your q on the TAC a while back. Enjoy the boeing.