Marty, the length of your rope has nothing to do with the throwing of the shotline; just in the setting of the rope itself which is pulling a rope up and over- not skill-dependent, for the most part.
From what I can gather, it appears your supervisors need to provide you with a bigshot. If they expect throwing accuracy above 50 feet, they're dreaming. There's a point where using a bigshot becomes a better choice.
I take a great deal of pride in my throwing accuracy, but I know full well that after the 40-50 foot range, a drain becomes more about luck than skill. This is where you move on to a mode that accuracy can once again rely on your talent, not a wish and silent begging to the shrew gods. At 50 foot+, I will make a throw attempt, but realistically in my mind I know it's more of a forceful 'Hail Mary' throw punctuated with hope. You throw to a vicinity and hope the shotbag finds its mark. That's accepting a disadvantage, working below our true abilities.
Throwing accuracy diminishes with height, like they're inversely proportional to one another after a certain distance. One would likely never use a bigshot on a 25 foot limb, nor would one use a throw on a 75 foot target crotch, not if you want consistent success. Like anything in the treecare profession, the right tool for the job at hand.
I'm not sure what your supervisors are thinking, not providing you with a bigshot. You, a climber, and two supervisors, standing around and no treecare getting done. Enough time and money went down the rathole in that one single morning to cover the cost of a bigshot head. Please don't view this as an insult, it happens to all of us in one form or another.
This is why I suggest to our community, as professional technicians, that certain tools be viewed as investment, not as purchases or expenses. Time is money. You can look at it as time saved, or time not lost. At the end of the day its all the same. Feeling defeated and discouraged, or elated and successful, there is intrinsic value attached to that and we all want to be successful, confident winners because in a same-team setting, you win, everybody wins. EVERYONE can master this. We're all made of the same stuff.
Thank you for bringing that tribulation to us, Marty. It takes a certain amount of courage.