Making Thai Khanom Tang Teak (ขนม ถัง แตก) I desire to make Thai Khanom Tang Teak (in standard Thai: ขนม ถัง แตก);
It is a pancake-like dish made from a batter with the following recipe:

About one cup of White Rice flour
About 2 cups of Sugar (from white to brown spectrum, per personal preference)
About one tablespoon of baking powder
About one tablespoon of Pandan extract (made, as far as I understand, from crushing or grinding Pandan/ใบเตย leafs with water)
At least 500ml Coconut milk

From my personal impression, no plain water should be added so that liquid is derived primarily from coconut milk.
Making and serving as street food
From my experience it is typically served in such a way that when it is almost ready, it is topped with chilled roasted sesame (often black sesame), shredded coconut and some white sugar, and than folded (like a sandwich).
From recognizing how it is made and reading on Wikipedia, I understand that at least in some recipes, it is common to add eggs or egg whites, probably to make the pancake softer.
As of 2019 it is becoming rarer as street food in Thailand.
My problem
I, as one who generally avoid eating eggs and follow a primarily-vegan diet, want to know how to make it very soft and spongy, without adding eggs or egg whites.
When I tried to make Khanom Thang teak by a similar pattern it didn't swell enough and wasn't soft enough. Perhaps this is because I have added some water due to shortage in coconut milk, but maybe it is because I am wrong about the amount of baking powder and need to use a doubled amount of baking powder (perhaps letting the batter rest in the refrigerator for about 6 hours or so).
My question
How could I make a vegan Khanom Tang Teak swelling and soft similar to as if it contained eggs or egg whites?
While I have never tried this dish (it looks delicious though!), I did some research and think I have some suggestions on veganising it.
Watching how it's cooked (in some videos I found here), it reminded me a little of 'Dutch Baby Pancakes'. These pancakes don't use a raising agent like baking powder, but rather rely on cooking at a very high heat and with a well developed batter, and are essentially inflated by steam.
So here are some tips that I might try if I were you:

Replace the egg with aquafaba. Here is a recipe for vegan Dutch Baby Pancakes that users aquafaba. About 3 tablespoons of aquafaba can be substituted per egg in your original recipe. Aquafaba works by absorbing different starches and proteins from the chickpeas, giving it egg-like qualities. It will help trap the steam pockets during the cooking process, and give your pancake the structure/strength to stay puffed up. I've found that aquafaba generally takes a little extra whipping to give it the same qualities as a whipped egg white, so maybe consider beating your batter a little longer than you normally would.
Make sure your pan is hot. Like really hot.  Try and use a pan that can become very hot, and heat evenly, like a cast iron skillet. The pan should be preheated to the point where the batter immediately starts to sizzle and set as soon as it hits the pan. Also, the videos I saw used a lid, as this will trap in the steam and help your pancakes rise.
Make sure your rest your batter. It might feel counterintuitive given it's meant to be a relatively aerated batter, but resting can help strengthen and develop glutens/proteins and give your outcome a better structure. I don't know much about rice flour (except that there is no gluten in it), but from the videos I saw, it sounds like this batter is rested for a lot longer than a Dutch Baby Pancake (which usually rests for around a half hour, maybe a bit less). The videos I saw implied a 2-3 hour rest, so I'd say try that out! I imagine it will be a process to get the rest time just right.