Bush Hog does not list the SQ600 manual on their website but EP80W-90 Gear Oil is what all the Bush Hog manuals call for the gear boxes in the rotary cutters. The SQ160 five foot mower manual calls for 2 Quarts of EP80W-90 Gear Oil so you should be OK. :2cents:
Two quarts sounds correct. Typically the correct gear oil level will cover 1/2 the input shaft. Most have side plugs that set the level to the correct amount. If you overfill no problem as long as your vent plug is working properly.