modified sine wave will work just fine for any drill press i ever used
assuming it is a standard motor drive, and not some variable frequency varidrive type of unit.
1kwatt mod sine wave is probably marginal to start the motor effectively however if you loosen the drive belt it will startup ok, and once running you can tighten the belt and away you go.. just leave it running between holes?
1500watt would likely be very reliable at starting the thing without fussing with the belt.
if you have the 1000 watt inverter, i would say give it a try.
also starting the drill press will be much easier if the belt drive is set to the lowest spindle speed, if you are drilling little holes and have the belts setup on the higher speeds the starting will be much harder.
bob g