More fat!
Your recipe has two dairy components (half and half and whipping cream).
The half and half is half cream, half milk.
To increase the fat, experiment with using more cream and less half and half.
cooking.stackexchange.com/users/19/Joel Spolsky
Try churning longer, making sure that your churn container is thoroughly frozen.
cooking.stackexchange.com/users/51/Janelle
Eggs!
Try a recipe with eggs
(especially freshly plucked from the chickens you have living in your back yard as we do).
My wife and I discovered this butter pecan recipe a few months ago and were quite pleased.
We subsequently tried a chocolate recipe with eggs (as well as melted chocolate instead of powdered ) and were quite pleased with that as well.
Better than previous batches made sans egg.
cooking.stackexchange.com/users/358/raven
If you've got a frozen bowl type ice cream churn (like a Kitchen Aid) then the unwritten rule is to nearly freeze your batter before churning.
I like to keep the batter in the freezer until crystals form on top.
Then I'll take it out, and give it a good stir to raise the temperature just a wee bit to break up those crystals.
Then, and only then do I take the churning bowl out of the freezer.
There is enough "cold" in the bowl to absorb the latent heat of fusion, but not if you have to drop the temperature 5-10 degrees before it freezes.
cooking.stackexchange.com/users/1148/Chris Cudmore
Check to make sure that your running it long enough, and also that your container is cold enough at the start.
If it's too thin, likely you're not getting the ice cream cold enough while churning.
Make sure you put the container in the back of your freezer (often a little colder back there).
If it's still getting firmer, let it keep churning, you might just not be there yet.
Lower the temperature in the freezer (or use a deep freeze if you have one), to better chill the container.
Remove the container from the freezer at the last possible second.
cooking.stackexchange.com/users/161/acrosman
I'm not sure what you're finished ice cream product looks like, so this answer is based on conjecture, but I do have a few recommendations.
I think the main issue here is that the recipe calls for too much sugar.
If I were you I would reduce the sugar to about 3/4 cup.
Large amounts of sugar drastically lower the freezing point by interfering with recrystallization during freezing.
This would explain why you are unable to get the soft serve consistency that you are looking for.
It also explains the lack of creaminess because the ice cream is not able to freeze around the air, which is where the volume and creamy feel come from.
If that doesn't work, then I second the notion to try an egg custard base or to add more cream, but honestly it looks like the recipe already has plenty of fat.
Altering the fat content could be more damaging to the recipe because the proteins in dairy are essential to stabilizing air bubble formation in ice cream.
cooking.stackexchange.com/users/25608/Cooking Student
Add 1 ounce of alcohol or extract containing alcohol.
This makes it creamier.
cooking.stackexchange.com/users/26398/user26398
My ice cream doesn't feel creamy enough. I got the recipe from Good Eats, and I can't tell if it's just the recipe or that I'm just not getting my "batter" cold enough before I try to make it. I let it chill overnight in the refrigerator, but it doesn't always come out of the machine looking like "soft serve" as he said on the show - it's usually a little thinner.  Recipe:  http://www.foodnetwork.com/recipes/alton-brown/serious-vanilla-ice-cream-recipe/index.html
How can I make my Ice Cream "creamier"?
cooking.stackexchange.com
<ice-cream>
cooking.stackexchange.com/questions/12
cooking.stackexchange.com/users/26/BarrettJ
Add more fat (e.g. increase cream and reduce half and half), use eggs or add an ounce of alcohol or an exctract containing alcohol. Try churning the batter for longer and make sure the batter is almost frozen before churning. To cool the batter faster, reduce the freezer temperature. First of all, the container should be thoroughly frozen before churning. Try increasing the fat content, adding eggs or a small amount of alcohol.
Increase the quantity of fat in the mixture. Use eggs. Make sure the container is thoroughly frozen and that it is churning for long enough. Try adding a small amount of alcohol.