How much overrun do I get with a compressorless home ice cream machine?
I have a 1.5 qt cuisinart prefrozen-bowl style ice cream maker.

I haven't measured it specifically but eyeballing it I would say that my overrun is 50-75%.
I know that is a wide range but it seems to change depending on recipe, additions, and how long I let it churn.

My ice cream maker has performed well for 3 years now and I recommend it.

I suspect your instant melting problem may be because you are freezing the mixture on a flat surface it has too much surface area when you scrape it off. The serious eats experiment used ice cube trays which would help reduce this problem.

Personally I haven't done experiments to try and reduce overrun because I like overrun. The air gives a nice buffer that makes the product melt more slowly, gives a smoother texture, and makes it easier to taste added flavors. 

It also makes the ice cream less rich so I can eat more of it.