Yeah, I can see that being an issue. Luckily I have a chest freezer so it just sits in there waiting for me to use it.
The only other thing with that machine (especially w/ the custard recipe) is I found that you need to sort of keep scraping the inside wall of it while it’s rotating (I just use a butter knife) to get it all mixed together properly. Small price to pay though for homemade ice cream imo.
I absolutely LOVE frozen custard. We have a friend who used to bring down a couple gallons of it every time he visited Florida from Milwaukee.