Chris, I'm absolutly sure that You are able to reach much greater ranges easy. It doesn't require a great power. The style of a throw decides about it mainly. Of course the good stones also.
I'm not sure I can explain my technique in English, but I'll try shortly. I use the right hand. My legs stay on the shot direction about. I rotate the sling easly few (1-4) times using the forearm and wirst on 6 or 7 o'clock position. My body is supported on the right leg with inclination to working arm.
I start my shot with rotation of the hips with simultaneous transfer of the body to left leg, next goes the elbow, next forearm end last the whirst litle turned to up. Somethink like a multi-part flail rotated on the vertical axle which goes forward on a trolley.
Regarding Your formula, IMHO it will give the false result because my shots are more flat than 45 degree angle, maybe about 30 degree. This formula disregards a air resistance too.
Try these 5 sets of parameters, please:
Velocity = 150 m/s
Mass = 1 kg
1) Angle = 45° without air resistance
2) 45° with air resistance
3) 30° without air resistance
4) 30° with air resistance
5) 25° with air resistance
http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMoti...Compare the times and ranges, please.
Anyway I will try the times measure in future and I will write about it.
Jurek