If the ice cream mix is setting up but tending to leave a buttery coating in your mouth the best thing would be to try cutting back on the cream and replacing it with whole milk or half & half.
If it's a recipe that you've used in another machine with great success but it doesn't seem to in this one, it's probably a case of how long the frozen bowl is staying cold. I have used the freezer bowl ice cream attachment for KitchenAid machines and have been frustrated more times than not as it doesn't freeze up as it should.
Too much sugar can also be a culprit in the mix not freezing quick enough. Sugar doesn't freeze so a really sweet mix is going to be softer. You might try decreasing sugar content slightly....not too much or you will end up with an icier result (If adding fruit to ice cream, combine the chopped fruit with some sugar and cook just a little to allow the sugar to dissolve and the moisture to evaporate. The sugar soaking into the fruit will keep the fruit softer in the ice cream instead of forming icy chunks of fruit. Or, just mix in fruit preserves.)
Make sure that the mix is VERY cold, ideally chilled for several hours or overnight before it goes into the the freezer. If time isn't on your side, then quick-chill it in a metal bowl or container in an ice bath and stir frequently to help chill it throughout.
The primary indicator for most ice cream freezers is that the dasher starts to sound labored in its attempt to stir the mix. Or if cranking by hand, you start to sound labored in your attempt to crank it!
Another factor that can affect freezing of ice cream (although probably not the case in your instance since you don't have control of the speed) is the speed of the machine. In the case of the KitchenAid insulated bowl for freezing ice cream, they warn not to go faster than "stir" or the mix won't have a chance to freeze to the side of the bowl before the dasher scrapes it.
I would try one of their recipes with it to see if it freezes up firm enough without turning to butter and then compare differences between your current recipe and theirs, adjusting sugar, milk to heavy cream ratio, etc.
You covered the big differences. Everything else is going to be brand and manufacturing quality.
My opinion on the different types:
For small amounts and small budgets I really like my cuisinart with the prefrozen bowl. The bowl gets so cold in my chest freezer that I don't even have to take the time to chill my mixture if I'm in a hurry. It always has plenty of cold leftover.
The ice/salt type either hand cranked (that's what kids are for) or electric are nice if you need to make batches back to back. You can obviously refill them instead of refreezing a bowl.
I don't have experience with the self refrigerating variety as they are out of my budget for the occasional homemade ice cream.
Best Answer
Usually with compressor machines you just turn it on and get it super cold, then make sure the dasher is spinning before pouring in the mix. Make sure the mix is below 40°F (4C) beforehand. I also chill down the spoon, container I’m putting the ice cream in, and any add-in’s I’m adding to it. Then spin it until the motor starts slowing down, or until it gets to a firm soft-serve consistency. Enjoy!