The sling seems like it has a steeper learning curve and colorful failure modes, like breaking a sliding glass door or somesuch. You might have better luck with a fairly low draw-weight bow and some blunt rubber-tipped arrows.
My guess is that deer wouldn't be frightened by a drone but the sound is pretty annoying. Maybe it would be a good Pavlovian conditioning trigger to pair with some other deterrent.
Could you put sprinklers out there?
I'm lucky enough to be in a semi-rural area with only one neighbor within 200m. The deer come from a large area that is currently under development for an encroaching subdivision. That subdivision is about about 350m at the closest point today though it will eventually extend to my back fence. That sucks but the newest construction has taken more than 20 years to reach that point.
I have a bow and have considered that option but I think the lethality could be a problem or the possibility of injuring a fawn. I just want to keep them on the other side of the fence. I would employ a drone to chase them since that would be fun but my place is in a no-fly radius near a small airport so that isn't an option without assuming some risk.
There is too much ground to cover for sprinklers to be effective even though the paths are well-established. I have tried path modification but that just shifts the crossings back and forth along the fence line. I have nice native grasses and plants and some really tasty fruit trees so my place is attractive.
The slingshot does the trick for the times when they are less than 35m away. Farther than that it gets dicey and they will just stand still until one is hit before they amble off into the trees.
This sling has better range though there is a learning curve. That will be the fun part.