More specifically (as I understand it), the syn oil didn't transfer the heat out of the new gears as well. The oil actually runs cooler, but the gears and/or bearings run hotter (during break-in).
There's nothing wrong with the oil you used. Run it with confidence.
I prefer a High Mileage rated synthetic oil personally just as a little extra insurance to prevent/help prevent/slow down oil leaks. It's not a cure all for a bad oil seal but may slow or stop oil leaks from old seals. The 4.0 rear oil seal is not a great design so leaks are common.