Anyhow, The problem with the stove ashes building up and the lack of air can be sorted in one quick mod.
first make a new hole in the base of the stove (see pics) near to the front. Next, slope the sand *gently* down towards the front, then cover with approx 1/2" - 1" of Fire Cement to form a hard cap (keeping the sand in place, and the sand / ash separated).
(Please excuse the crudity of this model as I didn't have time to build it to scale or paint it.)
Right click + view image for full size (couldn't resize, used MS Paint for quickness)...
You will need to have some kind of easy to open / remove 'plug' or plate over the hole in the base. Two possible solutions are;
1) A flap plate on the external side, either spring loaded or secured by a locking mechanism (bolt, slide catch etc).
2) A simple cover over the hole on the inside, something along the lines of a cast iron pot / pan lid with an 'eye hook' on top. Can be simply moved out of the way with a long hooked tool.
Alternatively, a second flue damper fitted to the underside would work well, if you can source one.
This hole can also be used to supply additional air to the fire, solving that issue of leaving the door ajar. A few small holes in the cover should be enough to still allow you to control the burn via the front vent.
As the ashes build up, simply open the bottom cover and rake the ashes down from the back, into the hole. Use a large pot as an ash pan. The fire cement capping will make the job easier as it forms a hard smooth surface. An inverted hearth shovel or a simple metal 'T' shaped bar will mke a good ash scraper.
You may or may not need to raise up your grate by an inch or two for clearance (cant tell from your videos).
SS