Hi Natalie,
Tapioca flour (aka starch) should be a good replacement at the same amount. Some sources say 2 parts tapioca flour should be used in exchange for 1 part cornstarch. I have not made this pudding with tapioca flour, but with my experience using it in other things, I think 2X would be a little too much for this pudding. If using tapioca flour, the total cook time will be less, just 5-6 minutes from the start. Whisking is important, but at the end, don’t whisk as much, as tapioca flour can get sticky with too much stirring.
As for arrowroot, I would replace the 1/2 cup cornstarch with 1/4 cup plus 1 tablespoon of arrowroot. Arrowroot holds up to freezing, unlike cornstarch. Arrowroot does break down at higher temperatures, but should work fine with this pudding in a smaller amount.
If you do make it substituting another starch for cornstarch, we’d love to hear how it turned out.
Best, Mary