You're vague about what's available at a reasonable price in your area, but there are plenty of things that are used to make vegetable mash:
Root vegetables. (Turnip, parsnip, yams, sweet potatoes, rutabaga/swede, carrots)
Winter squash. (Pumpkin, butternut squash, acorn squash, etc.)
None are necessarily a direct replacement, as some are ...
First, potato starch is exactly what you don’t want to use.
In a very non-scientific way of describing it, potato starch is what you get when you remove almost all of the potato, leaving you with the pure starch, which shouldn’t taste even remotely like potato. (It’s a pure binder. For many uses, you can swap starches based on different plants, e.g. corn ...
I suspect that their banana pudding, even if made from off-the-shelf pudding mix, was made with significantly less liquid than called for on the box. The whipped cream will lend looseness to the mixture even if the starch gel in the pudding is quite thick.
Note the cleanly-defined scoops taken out of the bucket on the left. That pudding is thick.
BTW, I ...