That seems a little light on fluid to include the convertor / cooler and lines ,but it might be all that the complete system would hold , just seems a bit light to me though. If a pan drop will take almost 6 quarts ,i'd of thought there'd be more then another 3 quarts in the convertor / cooler and lines then that
Mine took 5-1/4 with just a pan drop.
Seems like I read somewhere where it said if the trans was removed, to turn trans on side and fill with 9 qts. fluid. Maybe somewhere on here.
Would be so much easier if you could pump the fluid through using the transmission itself until the fluid runs clean, then do the level check.
Not that cheap if using the OE fluid, though.
If I had any kind of warranty, I wouldn't use anything other than OE either, just in case. That said, I really wouldn't trust that the dealer would do the service properly either, but at least they might be on the hook if something went awry.