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.
This one could just be the recipe's fault. I see now that it has you pour, basically, boiling milk onto eggs and sugar. That's pretty unusual; it could well result in you cooking some of the egg (bad!) before it's all incorporated. In your case, it sounds like it didn't quite go that far: you may have managed to cook the custard just right by accident. It's not helping you, though, and it might result in disasters eventually, especially with smaller ratio of egg to hot milk in another recipe. A more normal process would be:
- heat but don't boil at least some of the the milk and cream with the sugar
- stir some of the heated milk into the eggs to bring them partially up to temperature
- stir the warmed eggs and milk back into the rest of the milk
- continue heating and stirring until thickened (this might take some time, but not 20 minutes)
These steps, for example, are generally what David Lebovitz says to do in the recipes in The Perfect Scoop. He's a well-respected pastry chef who's also become a bit of an authority on ice cream; I've had success with every recipe I've tried from his book. As an example, this brown bread ice cream recipe from his blog follows those steps.
As for the texture of the final ice cream, that might be because of your eggs. Recipes are calibrated for large eggs; jumbo eggs are bigger, probably about 5/4 the size of large eggs, so 7 jumbo yolks might have been about 9 large yolks. The eggs are what give French-style ice cream its smooth, silky texture, so additional egg will accentuate that. I'd try it with 5 or 6 yolks (effectively 6.25 or 7.5).
It sounds like the texture you describe may have also lacked air, which could also be due to a few other common things. This could be due to insufficient egg-beating, but that's not the usual way to get light, fluffy ice cream, so I'd hesitate to blame it. Churning in the ice cream maker (this is not the same as the previous egg-beating) is normally the primary source of air. If you don't churn it long enough in the ice cream maker, it won't be as airy. Assuming you have the type of ice cream maker with the pre-frozen vessel, it's also important that the vessel be cold enough; if the custard doesn't freeze thoroughly in there, it won't be able to hold the air.
The ripple is a separate question. Generally, if you want something like that to stay soft when frozen, the way to do it is to load it up with sugar. The frozen raspberries I've seen aren't in syrup; if yours weren't either, you just didn't have nearly enough sugar. Otherwise, I'd again blame the recipe; you could probably fix it with more sugar. You could also try keeping it in a warmer place (the door) in your freezer. As some related reading, Lebovitz has a great blog post on making ice cream softer - note that sugar content is one of the methods. He also mentions use of stabilizers and anti-crystallization agents in ice cream; the same kinds of things are used in commercial versions of things like this ripple.
So, be wary of online recipes; they're not always the best, and sometimes they're not even well-tested, especially with something like ice cream that most people don't make. And once you get the basics down (e.g. learn the process from someone very trustworthy like Lebovitz), you can take a recipe online, keep the ingredient list, and prepare it the way you know works, ignoring some of the listed steps.
Best Answer
A few possibilities, hard to say given the amount of detail:
See also What determines whether a sherbet will set or not? and Is there a magic ingredient that keeps ice-cream soft?, among many other past questions on soft sorbet/sherbet/ice cream.